Computer Architecture

1
ComputerArchitecture

• EEL 4713/5764, Spring 2006
• Dr. Michael Frank
• Module 5 Computer Performance

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Part IBackground and Motivation
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I Background and Motivation

• Provide motivation, paint the big picture,
  introduce tools
• Review components used in building digital
  circuits
• Present an overview of computer technology
• Understand the meaning of computer performance
• (or why a 2 GHz processor isnt 2? as fast as
  a 1 GHz model)

Topics in This Part
Chapter 1 Combinational Digital Circuits
Chapter 2 Digital Circuits with Memory
Chapter 3 Computer System Technology
Chapter 4 Computer Performance
4
4 Computer Performance

• Performance is key in design decisions also cost
  and power
• It has been a driving force for innovation
• Isnt quite the same as speed (higher clock
  rate)

Topics in This Chapter
4.1 Cost, Performance, and Cost/Performance
4.2 Defining Computer Performance
4.3 Performance Enhancement and Amdahls Law
4.4 Performance Measurement vs Modeling
4.5 Reporting Computer Performance
4.6 The Quest for Higher Performance
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Course Instructional Objective 1

• As the syllabus says
• At the completion of this course, students should
  be able to
• CIO 1. (Metrics) Calculate and interpret
  different performance and cost metrics of
  computer systems.
• This CIO should also support the following
  Program Outcome
• Students graduating from the BSEE and BSCpE
  degree programs will have
• PO (a). (Apply) An ability to apply knowledge of
  mathematics, science and engineering
• PO (e). (Solve) An ability to identify,
  formulate, and solve engineering problems
• PO (o). (Topics) EE A knowledge of electrical
  engineering applications selected from the
  digital systems areas CpE A knowledge of
  computer science and computer engineering topics
  including computer architecture.
• Under assessment instruments, the syllabus
  says
• 1. Metrics. Students will solve exam problems in
  which they must analyze descriptions of
  hypothetical processors to determine their
  performance, cost-performance, and
  power-performance.

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Module Instructional Objectives

• I break down the CIO as follows
• CIO 1. Metrics (aeo). Calculate and interpret
  different performance and cost metrics of
  computer systems.
• 1.1. Know apply (a) the definitions of clock
  frequency, MIPS, execution time, performance,
  throughput, cost-performance, and
  power-performance.
• 1.2. Explain why a given metric is or is not
  appropriate to use in a given situation.
• 1.3. Identify (e.i) the specific figure(s) of
  merit that are most appropriate for choosing
  between alternative computer designs in a given
  scenario.
• 1.4. Formulate (e.ii) appropriate symbolic
  equations for calculating a desired figure of
  merit from the provided information about an
  architectural scenario.
• 1.5. Solve (e.iii) problems involving the
  determination of which of several computer
  designs would be preferable in a given scenario.
• 1.6. Apply Amdahls Law (and generalizations
  thereof) in characterizing the relationship
  between an improvement to a particular component
  of a system and the overall improvement of the
  whole system.
• 1.7. Apply (a) the CPU Performance Equation that
  relates performance and execution time to
  instruction count, CPI, and clock frequency.

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Topic 1

• Overview of Some Important Metrics for Computer
  SystemsPerformance, Cost, and Power Consumption

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Important Performance Metrics

• Some metrics that are often used, but that do not
  always accurately reflect true performance
• CPU clock frequency number of CPU clock cycles
  per unit time
• MIPS rating How many Millions of Instructions
  Per Second
• Benchmark ratings (e.g., SPECmarks) more on
  this later
• Metrics that are true measures of performance
• Total execution time of a work unit (on real
  applications)
• Wall-clock time from beginning to end of the
  execution process
• Performance 1/(execution time)
• For a single work unit
• Throughput ( work units)/(execution time)
• A generalized kind of performance

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Cost and Cost-Related Metrics

• In the real world, the performance of a system is
  not the only thing that is important
• For example, its cost may also matter a lot!
• E.g., the IBM Blue Gene/L has really high
  performance, but youre not likely to buy it as
  your next computer
• We almost always have budgetary constraints.
• The usual goal Maximize the cost-performance
  (i.e., cost-efficiency) of the systems that you
  buy.
• Cost-performance (performance) / (cost).
• In other words, you want to get the best value
  for your dollar.
• This strategy roughly maximizes total throughput
  within a fixed budget.
• Whenever you can have many systems gathered
  together working in parallel.

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Throughput and Cost-Performance

• When there is a fixed budget, the maximum
  throughput of a parallel system is (roughly) ?
  the cost-performance of the individual serial
  units.

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The Vanishing Computer Cost
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Cost/Performance
Figure 4.1 Performance improvement as a
function of cost.
 
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Importance of Power Consumption

• In the real world, a computers performance and
  manufacturing cost are not the only important
  concerns
• Operating costs, usability, and other factors may
  also be important!
• Today, power consumption is an increasingly
  important factor that impacts all of the
  following
• Manufacturing cost, operating cost, performance,
  and usability!
• In general, higher power consumption means
• More manufacturing cost
• for more aggressive power-delivery cooling
  systems
• power supplies, heat sinks, fans, etc.
• Higher operating cost
• More electricity consumed, frequent
  changing/recharging of batteries, inconvenience
  to user
• Lower performance
• Higher performance would exceed limits of cooling
  system
• Poor usability / poorer overall quality of
  product
• Annoyingly noisy cooling fans or data center A/C
  units, laptops that burn up your lap
• So in many design scenarios, we may wish to
  maximize performance within a fixed power budget,
  or minimize power consumption to reach a desired
  performance.

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Throughput and Power-Performance

• When there is a fixed power budget, the maximum
  throughput of a parallel system is (roughly) ?
  the power-performance of the individual serial
  units.
• This is exactly analogous to the earlier
  cost-performance analysis.

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Performance Maximizationwithin Cost and Power
Constraints

• Suppose we have both a cost budget and a power
  budget,
• and we want to maximize system throughput.
• With a given unit design, we must maximize the
  number of units.
• Then we have the following constraints on nunits
• nunits ? Cunit Cmax
• So, nunits ? Cmax/Cunit ?
• nunits ? Punit Pmax
• and nunits ? Pmax/Punit ?
• The largest value of nunits within these
  constraints is
• nunits min( ? Cmax/Cunit ?, ? Pmax/Punit ? )
  ? min( Cmax/Cunit, Pmax/Punit) ?
• and so the maximum feasible throughput is
• Ttot Tunit ? nunits Tunit ?
  ?min(Cmax/Cunit,Pmax/Punit)?

C cost P power T throughput
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Power-Performance and Energy Efficiency

• Power-performance means performance (i.e.,
  throughput) per unit of power consumption
• power-performance (throughput)/(power).
• Of course, since
• throughput (work units)/(time) and
• power (energy consumed)/(time),
• The times cancel, and so power-performance is
  equal to
• (work units)/(energy consumed)
• In other words, system power-performance is the
  same thing as the energy efficiency of the
  underlying computing process.
• To maximize power-performance, minimize the
  amount of energy that is consumed per unit of
  work that is performed.

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System Optimization Example

• Suppose you have a budget of 1M to set up a new
  corporate data center that should have a total
  power consumption of no more than 100kW while
  serving web transactions in a simple database
  application. If your goal is to maximize total
  performance (in transactions/second) while
  staying within your budget and meeting the power
  constraint, which of the following types of
  machines would be preferable as a basis for the
  design?
• Sun servers, each 15,000, burning 100W,
  processing 100 transactions/second
• Playstation 2s, each 100 from flea market, 30W,
  processing 30 transactions/second
• Solution
• A PS2-based design could attain 50? higher
  throughput and use only 1/3 of the budget while
  still meeting the power constraints!

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Topic 2

• Measuring Computer Performance

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4.2 Defining Computer Performance
Figure 4.2 Pipeline analogy shows that
imbalance between processing power and I/O
capabilities leads to a performance bottleneck.
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Concepts of Performance and Speedup

• Performance 1 / Execution time
  is simplified to
• Performance 1 / CPU execution time
• (Performance of M1) / (Performance of M2)
  Speedup of M1 over M2
• (Execution time on M2) / (Execution time
  on M1)
• Terminology M1 is x times as fast as M2 (e.g.,
  1.5 times as fast)
• M1 is 100(x 1) faster than M2 (e.g., 50
  faster)
• CPU time (Clock cycles executed) ? (Time per
  cycle)
• Instructions ? (Cycles per instruction)
  ? (Time per cycle)
• Instructions ? CPI / (Clock frequency)
• Instruction count, CPI, and clock rate are not
  completely independent, so improving one by a
  given factor may not lead to overall execution
  time improvement by the same factor.

CPU performance equation
 
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Faster Clock ? Shorter Running Time
Figure 4.3 Faster steps do not necessarily
mean shorter travel time.
 
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4.3 Performance Enhancement Amdahls Law
f fraction unaffected p speedup
of the rest
Figure 4.4 Amdahls law speedup achieved if
a fraction f of a task is unaffected and the
remaining (1f) part runs p times as fast.
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Amdahls Law Used in Design
Example 4.1

• A processor spends 30 of its time on flp
  addition, 25 on flp mult,
• and 10 on flp division. Evaluate the following
  enhancements, each
• costing the same to implement
• Redesign of the flp adder to make it twice as
  fast.
• Redesign of the flp multiplier to make it three
  times as fast.
• Redesign the flp divider to make it 10 times as
  fast.
• Solution
• Adder redesign speedup 1 / 0.7 0.3 / 2
  1.18
• Multiplier redesign speedup 1 / 0.75 0.25 /
  3 1.20
• Divider redesign speedup 1 / 0.9 0.1 / 10
  1.10
• What if both the adder and the multiplier are
  redesigned?

 
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4.4 Performance Measurement vs. Modeling
Figure 4.5 Running times of six programs on
three machines.
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Performance Benchmarks
Example 4.3

• You are an engineer at Outtel, a start-up
  aspiring to compete with Intel
• via its new processor design that outperforms the
  latest Intel processor
• by a factor of 2.5 on floating-point
  instructions. This level of performance
• was achieved by design compromises that led to a
  20 increase in the
• execution time of all other instructions. You are
  in charge of choosing
• benchmarks that would showcase Outtels
  performance edge.
• What is the minimum required fraction f of time
  spent on floating-point instructions in a program
  on the Intel processor to show a speedup of 2 or
  better for Outtel?
• Solution
• We use a generalized form of Amdahls formula in
  which a fraction f is speeded up by a given
  factor (2.5) and the rest is slowed down by
  another factor (1.2) 1 / 1.2(1 f) f /
  2.5 ? 2 ? f ? 0.875

 
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Performance Estimation
Average CPI ?All instruction classes (Class-i
fraction) ? (Class-i CPI) Machine cycle time
1 / Clock rate CPU execution time
Instructions ? (Average CPI) / (Clock rate)
Table 4.3 Usage frequency, in percentage, for
various instruction classes in four
representative applications.
Application ? Instrn class ? Data compression C language compiler Reactor simulation Atomic motion modeling
A Load/Store 25 37 32 37
B Integer 32 28 17 5
C Shift/Logic 16 13 2 1
D Float 0 0 34 42
E Branch 19 13 9 10
F All others 8 9 6 4
 
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MIPS Rating Can Be Misleading
Example 4.5

• Two compilers produce machine code for a program
  on a machine
• with two classes of instructions. Here are the
  number of instructions
• Class CPI Compiler 1 Compiler 2
• A 1 600M 400M
• B 2 400M 400M
• What are run times of the two programs with a 1
  GHz clock?
• Which compiler produces faster code and by what
  factor?
• Which compilers output runs at a higher MIPS
  rate?
• Solution
• Running time 1 (2) (600M ? 1 400M ? 2) / 109
  1.4 s (1.2 s)
• b. Compiler 2s output runs 1.4 / 1.2 1.17
  times as fast
• c. MIPS rating 1, CPI 1.4 (2, CPI 1.5) 1000
  / 1.4 714 (667)

 
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4.5 Reporting Computer Performance
Table 4.4 Measured or estimated execution
times for three programs.
Time on machine X Time on machine Y Speedup of Y over X
Program A 20 200 0.1
Program B 1000 100 10.0
Program C 1500 150 10.0
All 3 progs 2520 450 5.6
Analogy If a car is driven to a city 100 km away
at 100 km/hr and returns at 50 km/hr, the average
speed is not (100 50) / 2 but is obtained from
the fact that it travels 200 km in 3 hours.
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Comparing the Overall Performance
Table 4.4 Measured or estimated execution
times for three programs.
Time on machine X Time on machine Y Speedup of Y over X
Program A 20 200 0.1
Program B 1000 100 10.0
Program C 1500 150 10.0
Speedup of X over Y
10 0.1 0.1
Arithmetic mean
6.7
3.4
Geometric mean
2.15
0.46
Geometric mean does not yield a measure of
overall speedup, but provides an indicator that
at least moves in the right direction
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4.6 The Quest for Higher Performance
State of available computing power ca. the early
2000s Gigaflops on the desktop Teraflops in
the supercomputer center Petaflops on the
drawing board Note on terminology (see Table
3.1) Prefixes for large units Kilo 103,
Mega 106, Giga 109, Tera 1012, Peta
1015 For memory K 210 1024, M 220,
G 230, T 240, P 250 Prefixes for small
units micro 10-6, nano 10-9, pico
10-12, femto 10-15
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Supercom-puters
Figure 4.7 Exponential growth of
supercomputer performance.
 
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The Most Powerful Computers
Figure 4.8 Milestones in the DOEs
Accelerated Strategic Computing Initiative (ASCI)
program with extrapolation up to the PFLOPS
level.
 
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Performance is Important, But It Isnt Everything
Figure 25.1 Trend in energy consumption per
MIPS of computational power in general-purpose
processors and DSPs.
 
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Computer Architecture Lecture Notes Spring
2005Dr. Michael P. Frank

• Competency Area 2
• Performance Metrics
• Lecture 1

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Performance Metrics

• Why is it necessary for us to study performance?
• Performance is usually the key to the
  effectiveness of a system (hardware software).
• Performance is critical to customers
  (purchasers), thus, we as designers and
  architects must also make it a priority.
• Performance must be assessed and understood in
  order for a system to communicate efficiently
  with peripheral devices.

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Topic Computer Performance

• Sub-Topic Airplane Analogy

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Performance Metrics

• How can we determine performance?

Consider this example from the transportation
industry
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Performance Example

• Fuel Capacity in liters
• Range in kilometers
• Speed in kilometers/hour
• Throughput is defined as
• ( of passengers) x (cruising speed)
• Cost is given as
• (fuel capacity) / (passengers x range)
• Which mode of transportation has the best
  performance?

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Performance Example

• It depends on how we define performance.
• Consider raw speed
• Getting from one place to another quickly

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Performance Example

• What if were interested in the rate at which
  people are carried throughput

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Performance Example

• Often times we relate performance and cost. Thus
  we can consider the amount of fuel used per
  passenger

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Topic Computer Performance

• Sub-Topic Basic Concepts Performance,
  Throughput, and Execution Time

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Performance Metrics

• Similar measures of performance are used for
  computers.
• Number of computations done per unit of time
• Cost of computations
• Possibly several aspects of cost can be
  considered including initial purchase price,
  operating cost, cost of training users of system,
  etc.
• Common performance measures are
• RESPONSE TIME the amount of time it takes a
  program to complete (a.k.a execution time)
• THROUGHPUT the total amount of work done in a
  given amount of time

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Performance Metrics

• Example
• Given the following actions
• 1. Replacing processor with a faster version
• 2. Adding additional processors to perform
  separate tasks in a multiprocessor system
• do they (a) increase throughput, (a) decrease
  response time or (c) both?

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Defining Performance

• Our focus will be primarily on execution time.
• To maximize performance implies a minimization in
  execution time
• For two machines
• We say that machine Y is faster than machine X.

46
Performance Metrics

• Notes

(1) If X is n times faster than Y, then

• To avoid confusion, well use the following
  terminology
• We say We mean
• improve performance ? increase
  performance
• improve execution time ? decrease execution
  time

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Performance Example
If machine A runs a program in 10 seconds and
machine B runs the same program in 15 seconds,
how much faster is A than B?
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Performance Example
If machine A runs a program in 10 seconds and
machine B runs the same program in 15 seconds,
how much faster is A than B?
49
Topic Computer Performance

• Sub-Topic Measuring Performance

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Measuring Performance

• Quite simply, TIME is the measure of computer
  performance!
• The most straightforward definition of time is
  wall-clock time ? elapsed time ? response time.

Total time to complete a task including system
overhead activities such as Input/Output tasks,
disk and memory accesses, etc.
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Measuring Performance

• CPU Time is the time it takes to complete a task
  excluding the time it takes for I/O waits.

CPU TIME
USER CPU TIME The time CPU is busy executing the
users code.
SYSTEM CPU TIME The time CPU spends performing
operating system tasks.
Note Sometimes system and user CPU times are
difficult to distinguish since it is hard to
assign responsibility for OS activities.
52
Measuring Performance

• Example,
• To understand the concept of CPUTime, consider
  the UNIX command time. Once typed, it may
  return a response similar to
• 90.7u 12.9s 239 65
• What do these numbers mean?

53
Measuring Performance

• Example,
• To understand the concept of CPUTime, consider
  the UNIX command time. Once typed, it may
  return a response similar to
• 90.7u 12.9s 239 65

of elapsed time that is CPU time
User CPU Time
System CPU Time
Elapsed Time
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Measuring Performance

• Example,
• To understand the concept of CPUTime, consider
  the UNIX command time. Once typed, it may
  return a response similar to
• 90.7u 12.9s 239 65
• What is the total CPUTime?
• Percentage of time spent on I/O and other
  programs?

55
Measuring Performance

• Example,
• To understand the concept of CPUTime, consider
  the UNIX command time. Once typed, it may
  return a response similar to
• 90.7u 12.9s 239 65
• What is the total CPUTime?
• Percentage of time spent on I/O and other
  programs?

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Measuring Performance

• Other notes
• SYSTEM PERFORMANCE reciprocal of elapsed time
  on an unloaded system (e.g. no user applications)
• CPU PERFORMANCE recip. of user CPU time
• CLOCK CYCLES (CC) discrete time intervals
  measured by the processor clock running at a
  constant rate.
• CLOCK PERIOD time it takes to complete a clock
  cycle
• CLOCK RATE inverse of clock period

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Measuring Performance

• Consider CPU performance
• Also,

58
Measuring Performance

• Since the execution time clearly depends on the
  number of instructions for a program, we must
  also define another performance metric
• CPI average number of clock cycles
• per instruction

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Measuring Performance

• Now we have two more equations that we can define
  for CPUTime

60
Measuring Performance

• In summary, performance metrics include

Components of Performance Units of Measure
CPUTime Seconds for program
IC of instructions for a program
CPI Average of clock cycles per instructions
tCC Seconds per clock cycle
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Measuring Performance

• Example,
• Suppose Machine A implements the same ISA as
  Machine B. Given and
• for some program, and
• and for the same program, determine
  which machine is faster and by how much.

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Breakdown by Instruction Category

• Recall CPI Clock cycles (CC) per instruction
• But, CPI depends on many factors, including
• Memory system behavior
• Processor structure
• Availability special processor features
• E.g., floating point, graphics, etc.
• To characterize the effect of changing specific
  aspects of the architecture, we find it helpful
  to break down CC into components due to different
  classes (categories) of instructions
• Where
• ICi instruction count for class i
• CPIi avg. cycles for insts. in class i
• n the number of instruction classes

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Example

• Suppose a processor has 3 categories of
  instructions A,B,C with the following CPIs
• And, suppose a compiler designer is comparing two
  code sequences for a given program that have the
  following instruction counts
• Determine
• (i) Which code sequence executes the most
  instructions?
• (ii) Which will be faster?
• (iii) What is the average CPI for each code
  sequence?

Instr. Class CPIi
A 1
B 2
C 3
Code Seq. Inst. counts Inst. counts Inst. counts
Code Seq. ICA ICB ICC
1 2 1 2
2 4 1 1
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Solution to Example

• Part (i)
• ICseq1 2 1 2 5 instructions
• ICseq2 4 1 1 6 instructions
• ? Code sequence 2 executes more instructions
• Part (ii)
• CCseq1 ?i(CPIixICi) 1x2 2x1 3x2 10
  cycles
• CCseq2 ?i(CPIixICi) 1x4 2x1 3x1 9
  cycles
• ? Code sequence 2 takes fewer cycles ? is faster!
• Part (iii)
• CPIseq1 CC/ICseq1 10 cyc./5 inst. 2
• CPIseq2 CC/ICseq2 9 cyc./6 inst. 1.5
• Which part should we consult to tell us which
  code sequence has better performance?

65
Topic Computer Performance

• Subtopic
• Benchmarks Performance Summaries

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Importance of Benchmarks

• How do we evaluate and compare the performance of
  different architectures?
• We use benchmarks
• Programs that are specifically chosen to measure
  performance.
• A workload is a set of programs.
• Benchmarks consist of workloads that (user hopes)
  will predict the performance of the actual
  workload
• It is important that benchmarks consist of
  realistic workloads
• Not simple toy programs or code fragments
• Manufacturers often try to fine-tune their
  machines to do well on popular benchmarks that
  were too simple
• This does not always mean the machine will do
  well on real programs!

67
SPEC benchmark

• A popular source of benchmarks is SPEC
• Standard Performance Evaluation Corporation
• General CPU benchmarks CPU2000.
• Includes programs such as
• gzip (compression), vpr (FPGA place route), gcc
  (compiler), crafty (chess), vortex (database)
• SPEC also offers specialized benchmarks for
• Graphics, Parallel computing, Java, mail servers,
  network fileservers, web servers
• They publish reports on benchmark results for
  various systems.
• Main metric SPECRatio Proportional to average
  inverse execution time. The bigger, the better!
• Reproducibility of results is very important!

68
Summarizing Performance

• How do we summarize performance in a way that
  accurately compares different machines?
• One common approach Total Execution Time (TET)
• Based on
• Or, if the workload includes n different
  programs, we can calculate the average or
  Arithmetic Mean (AM)
• Smaller AM ? Improved performance
• Other methods are also used
• Weighted arithmetic mean, geometric mean ratio.

69
Topic Computer Performance

• Subtopic Performance Improvementand Amdahls
  Law

70
Performance Improvement

• Recall the formula CPUTime IC CPI / fcyc.
• Thus, CPU performance is Perf f / (ICCPI).
• Thus we can see 3 basic ways to improve CPU
  performance on a given task
• Increase clock frequency
• Decrease CPI
• by improved processor organization
• Decrease instruction count
• By compiler enhancement,
• change in ISA design (new instructions), or
• A more efficient application algorithm.
• However, we have to be careful!
• Sometimes, improving one of these can hurt others!

71
Generalized Cost Measures

• In this course, we will often be focusing on ways
  to minimize execution time of programs.
• Either CPU time, or number of clock cycles.
• Execution time is one example of what we may call
  a generalized cost measure (GCM).
• A GCM is any property of a HW/SW design that
  tells us how much of some valued resource is used
  up when the system is manufactured or used.
• Other examples of important GCMs include
• Energy consumed by a computation
• Silicon chip area used up by a circuit design
• Dollar cost to manufacture a computer component
• We will study some general engineering principles
  that apply to the minimization of any GCM in any
  system.

72
Additive Cost Measures

• Let us suppose we have a GCM C for a system.
• Many times, the total cost C can be represented
  as a sum of independent cost components
• E.g., C C1 C2 Cn or .
• These could correspond to the resources used by
  individual subsystems of the whole system.
• Or, used in doing particular categories of tasks.
• For example, execution time T can be broken down
  as the sum of time Tfp taken by floating-point
  instructions and the time Toth for others.
• That is, T Tfp Toth.

73
Improving Part of a System

• Suppose a GCM is broken down as C A B.
• The total cost is the sum of two components A
  B.
• Now suppose you are considering making an
  improvement to the system design that affects
  only cost component B.
• Suppose you reduce it by a factor f, to B' B/f.
• The new total cost is then C' A B'.
• The cost of component A is unaffected.
• Overall (total) cost has therefore been reduced
  by the factor

74
Diminishing Returns

• Suppose we continue improving (reducing) a cost
  component by larger and larger factors.
• Does this mean the systems total cost will be
  reduced by correspondingly large factors? ? NO!
• Even if we improved one cost component (B in our
  example) by a factor of f 8, note that
• Even here, the overall cost reduction factor
  foverall would still be only the finite value
  1B/A!
• The system can only be improved by at most this
  factor, if we improve just the one component B.

75
Diminishing Returns Example

• Suppose a particular chip contains B 1 cm2 of
  logic circuits, and A 2 cm2 of cache memory.
• The total cost (in terms of area) is C AB 3
  cm2.
• Now, lets go crazy trying to simplify and shrink
  the design of just the logic circuit
• What is the maximum factor by whichthis tactic
  can reduce the area cost of the whole design
  (logicmemory)?
• Obviously, this can reduce the total area from 3
  (cm2) to no less than 2 (area of memory alone),
• or, shrink it by a factor of foverall 3/2
  1.5.
• Note we could have obtained this same answer
  using the equation foverall,max 1B/A as well.

Logic1 cm2
Memory2 cm2
76
Graph Showing Diminishing Returns
Part/rest (initial)
(B/A)
( f )
77
Important Lessons to Take from This

• Its probably not worth spending significant
  design time extensively improving just a single
  component of a system,
• Unless that component accounts for a dominant
  part of the total cost (by some measure) to begin
  with.(B/A gtgt 1).
• Its only worth improving a given component up to
  the point where it is no longer dominant.
• Reducing it further wont make a lot of
  difference.
• Therefore, all components with significant costs
  must be improved together in order to
  significantly improve an entire design.
• Well-engineered systems will tend to have roughly
  comparable costs in all of their major components.

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Other Ways to Calculate foverall

• Earlier, we saw this formula
• For the overall improvement factorfoverall
  resulting from improvingcomponent B by the
  factor f.
• But, what if we dont know the values of A and B?
  
• What if we only know their relative sizes?
• Fortunately, it turns out that we can still
  calculate foverall.
• Let us define fracenh B/C B/(AB) to be the
  fraction of the original total system cost that
  is accounted for by the particular part B that is
  going to be enhanced.
• Then, the fraction of cost accounted for by A
  (the rest of the system) is
• Our equation for foverall can then be reexpressed
  in terms of the quantities fracenh and 1-fracenh,
  as follows

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Calculating foverall in terms of fracenh

• Lets re-express foverall in terms of fracenh
• We will call this form for foverall the
  Generalized Amdahls Law. (Well see why in a
  moment.)

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Amdahls Law Proper

• We saw that execution time is one valid cost
  measure.
• In such a case, note that the factor by which a
  cost is reduced is the speedup, or the factor by
  which performance is improved.
• We thus rename the improvement factor f of B
  (the enhanced part) to speedupenh, and the
  overall improvement factor foverall becomes
  speedupoverall, and we get
• This is called Amdahls Law, and it is one of the
  most widely hyped quantitative principles of
  processor design.
• But as we can see, it is not a special law of CPU
  architecture, but just an application of the
  universal engineering principle of diminishing
  returns which we discussed earlier.

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Key Points from This Module

• Throughput vs. Response Time
• Performance as Inverse Execution Time
• Speedup Factors
• Averaging Benchmark Results
• CPU Performance Equation
• Execution time IC CPI tcc
• Performance fcc / (IC CPI)
• Amdahls Law
• C' A B/f
• Implies

C Execution time after improvement B Part of
execution time affected by improvement f Factor
of improvement (speedup of enhanced part) A
Part of execution time unaffected by improvement
82
Example Performance Calculation

• Suppose program takes 10 secs. on computer A
• And suppose computer A has a 4 GHz clock
• Want new computer B to run prg. in 6 seconds.
• Suppose that increasing the clock speed is only
  possible with a substantial processor redesign,
• which will result in 1.2 as many clock cycles
  being needed to execute the program.
• What clock rate is needed?
• Answer 4 GHz (10/6) 1.2 8 GHz

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Another Example

• Consider two different implementations of a given
  ISA, running a given benchmark
• Processor A has a cycle time of 250 ps
• And a CPI of 2.0
• Processor B has a cycle time of 500 ps
• And a CPI of 1.2
• Which computer is faster on this benchmark, and
  by what factor?
• Processor A takes 250 ps 2.0 500 ps / instr.
• Processor B takes 500 ps 1.2 600 ps / instr.
• Thus, A is faster by a factor of 6/5 1.2.

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Another example

• Suppose some Java application takes 15 seconds on
  a certain machine.
• A new Java compiler is released that requires
  only 0.6 as many dynamic instructions to run the
  application.
• Unfortunately, it also increases the CPI by 1.1
  
• Presumably, uses more multi-cycle instructions.
• How fast will the application run when compiled
  using the new compiler?
• It will take 15 0.6 1.1 9.9 seconds to run
• It will be 15/9.9 50/33 1.515 faster
• Only slightly more than 50 faster than before.

85
Another Example

• Consider the following measurements of execution
  time
• Which of the following statements are true?
• A is faster than B for program 1.
• A is faster than B for program 2.
• A is faster than B for a workload with equal
  numbers of executions of programs 1 and 2.
• A is faster than B for a workload with twice as
  many executions of program 1 as of program 2.

Program Computer A Computer B
1 2 sec. 4 sec.
2 5 sec. 2 sec.