CPU Performance Evaluation:
Cycles Per Instruction (CPI)
• Most computers run synchronously utilizing a CPU clock running at
a constant clock rate: Or clock frequency: f
Clock cycle
where:
Clock rate = 1 / clock cycle
f
•
•
CPI
= 1 /C
cycle 1
cycle 2
cycle 3
The CPU clock rate depends on the specific CPU organization (design) and
hardware implementation technology (VLSI) used.
A computer machine (ISA) instruction is comprised of a number of elementary
or micro operations which vary in number and complexity depending on the
the instruction and the exact CPU organization (Design).
– A micro operation is an elementary hardware operation that can be
performed during one CPU clock cycle.
– This corresponds to one micro-instruction in microprogrammed CPUs.
– Examples: register operations: shift, load, clear, increment, ALU
operations: add , subtract, etc.
•
Thus: A single machine instruction may take one or more CPU cycles to
complete termed as the Cycles Per Instruction (CPI).
Instructions Per Cycle = IPC = 1/CPI
•
Average (or effective) CPI of a program: The average CPI of all instructions
executed in the program on a given CPU design.
4th Edition: Chapter 1 (1.4, 1.7, 1.8)
3rd Edition: Chapter 4
Cycles/sec = Hertz = Hz
MHz = 106 Hz GHz = 109 Hz
EECC550 - Shaaban
#1 Lec # 3
Winter 2012 12-4-2012
Generic CPU Machine Instruction Processing Steps
Instruction
Obtain instruction from program memory
Fetch
The Program Counter (PC) points to the instruction to be processed
Instruction
Decode
Operand
Fetch
Determine required actions and instruction size
Locate and obtain operand data
From data memory or registers
Execute
Result
Compute result value or status
Store
Deposit results in storage (data memory or
register) for later use
Next
Determine successor or next instruction
Instruction
(i.e Update PC to fetch next instruction to be processed)
CPI = Cycles per instruction
EECC550 - Shaaban
#2 Lec # 3
Winter 2012 12-4-2012
Computer Performance Measures:
Program Execution Time
• For a specific program compiled to run on a specific machine
(CPU) “A”, has the following parameters:
– The total executed instruction count of the program. I
– The average number of cycles per instruction (average CPI). CPI
– Clock cycle of machine “A” C
Or effective CPI
•
How can one measure the performance of this machine (CPU) running
this program?
– Intuitively the machine (or CPU) is said to be faster or has better
performance running this program if the total execution time is
shorter.
– Thus the inverse of the total measured program execution time is
a possible performance measure or metric:
Seconds/program
Programs/second
PerformanceA = 1 / Execution TimeA
How to compare performance of different machines?
What factors affect performance? How to improve performance?
EECC550 - Shaaban
#3 Lec # 3
Winter 2012 12-4-2012
Comparing Computer Performance Using Execution Time
•
To compare the performance of two machines (or CPUs) “A”, “B”
running a given specific program:
PerformanceA = 1 / Execution TimeA
PerformanceB = 1 / Execution TimeB
•
Machine A is n times faster than machine B means (or slower? if n < 1) :
Speedup = n =
•
PerformanceA
PerformanceB
Example:
For a given program:
Execution time on machine A:
Execution time on machine B:
Speedup= Performance / Performance
A
B
=
Execution TimeB
Execution TimeA
(i.e Speedup is ratio of performance, no units)
ExecutionA = 1 second
ExecutionB = 10 seconds
= Execution TimeB / Execution TimeA
= 10 / 1 = 10
The performance of machine A is 10 times the performance of
machine B when running this program, or: Machine A is said to be 10
times faster than machine B when running this program.
The two CPUs may target different ISAs provided
the program is written in a high level language (HLL)
EECC550 - Shaaban
#4 Lec # 3
Winter 2012 12-4-2012
CPU Execution Time: The CPU Equation
• A program is comprised of a number of instructions executed , I
– Measured in: instructions/program AKA Dynamic Executed Instruction Count
• The average instruction executed takes a number of cycles per
instruction (CPI) to be completed.
Or Instructions Per Cycle (IPC):
– Measured in: cycles/instruction, CPI
IPC = 1/CPI
• CPU has a fixed clock cycle time C = 1/clock rate
– Measured in:
seconds/cycle
C
= 1/f
• CPU execution time is the product of the above three
parameters as follows: Executed
CPU time
= Seconds
Program
T =
execution Time
per program in seconds
= Instructions x Cycles
Program
Instruction
I x
Number of
instructions executed
x Seconds
CPI x
Average CPI for program
(This equation is commonly known as the CPU performance equation)
Cycle
C
CPU Clock Cycle
EECC550 - Shaaban
#5 Lec # 3
Winter 2012 12-4-2012
CPU Average CPI/Execution Time
For a given program executed on a given machine (CPU):
CPI = Total program execution cycles / Instructions count
Executed (I)
(i.e average or effective CPI)

CPU clock cycles = Instruction count x CPI
CPU execution time =
T
(executed, I)
= CPU clock cycles x Clock cycle
= Instruction count x CPI x Clock cycle
=
I
x CPI x
C
execution Time
per program in seconds
Number of
instructions executed
Average
or effective
CPI for
program
CPU Clock Cycle
(This equation is commonly known as the CPU performance equation)
CPI = Cycles Per Instruction
EECC550 - Shaaban
#6 Lec # 3
Winter 2012 12-4-2012
CPU Execution Time: Example
• A Program is running on a specific machine (CPU) with
I
the following parameters:
– Total executed instruction count: 10,000,000 instructions
– Average CPI for the program: 2.5 cycles/instruction.
– CPU clock rate: 200 MHz. (clock cycle = C = 5x10-9 seconds)
• What is the execution time for this program:
CPU time
= Seconds
Program
= Instructions x Cycles
Program
i.e 5 nanoseconds
x Seconds
Instruction
Cycle
CPU time = Instruction count x CPI x Clock cycle
= 10,000,000
x 2.5 x 1 / clock rate
= 10,000,000
x 2.5 x 5x10-9
= 0.125 seconds
Nanosecond = nsec =ns = 10-9 second
MHz = 106 Hz
T = I x CPI x C
EECC550 - Shaaban
#7 Lec # 3
Winter 2012 12-4-2012
Factors Affecting CPU Performance
CPU time
= Seconds
Program
T
=
= Instructions x Cycles
Program
x Seconds
Instruction
Cycle
Average
I
x CPI
x
C
Instruction Cycles per
Clock Rate
Count
(1/C)
Instruction
Program
Compiler
Instruction Set
Architecture (ISA)
Organization
(CPU Design)
Technology
(VLSI)
T = I x CPI x C
EECC550 - Shaaban
#8 Lec # 3
Winter 2012 12-4-2012
Aspects of CPU Execution Time
CPU Time = Instruction count executed x CPI x Clock cycle
T = I x CPI x C
Depends on:
Program Used
Compiler
ISA
Instruction Count
I
(executed)
Depends on:
Program Used
Compiler
ISA
CPU Organization
CPI
(Average
CPI)
Clock
Cycle
C
Depends on:
CPU Organization
Technology (VLSI)
EECC550 - Shaaban
#9 Lec # 3
Winter 2012 12-4-2012
Performance Comparison: Example
• From the previous example: A Program is running on a specific
machine (CPU) with the following parameters:
– Total executed instruction count, I: 10,000,000 instructions
– Average CPI for the program: 2.5 cycles/instruction.
– CPU clock rate: 200 MHz. Thus: C = 1/(200x106)= 5x10-9 seconds
• Using the same program with these changes:
– A new compiler used: New executed instruction count, I: 9,500,000
New CPI: 3.0
– Faster CPU implementation: New clock rate = 300 MHz
Thus: C = 1/(300x106)= 3.33x10-9 seconds
• What is the speedup with the changes?
Speedup
= Old Execution Time = Iold x
New Execution Time Inew x
CPIold
x Clock cycleold
CPInew
x Clock Cyclenew
Speedup = (10,000,000 x 2.5 x 5x10-9) / (9,500,000 x 3 x 3.33x10-9 )
= .125 / .095 = 1.32
or 32 % faster after changes.
Clock Cycle = C = 1/ Clock Rate
T = I x CPI x C
EECC550 - Shaaban
#10 Lec # 3
Winter 2012 12-4-2012
Instruction Types & CPI
•
Given a program with n types or classes of instructions executed on
given CPU with the following characteristics:
a
e.g ALU, Branch etc.
Ci = Count of instructions of typei executed
CPIi = Cycles per instruction for typei
Then:
i = 1, 2, …. n
Depends on CPU Design
CPI = CPU Clock Cycles / Instruction Count I
i.e average or effective CPI
Executed
Where:
n
CPU clock cycles  
i 1
CPI  C 
i
i
Executed Instruction Count I = S Ci
T = I x CPI x C
EECC550 - Shaaban
#11 Lec # 3
Winter 2012 12-4-2012
Instruction Types & CPI: An Example
• An instruction set has three instruction classes:
e.g ALU, Branch etc.
Instruction class
A
B
C
CPI
1
2
3
For a specific
CPU design
• Two code sequences have the following instruction counts:
Instruction counts for instruction class
A
B
C
2
1
2
4
1
1
Program
Code Sequence
1
2
• CPU cycles for sequence 1 = 2 x 1 + 1 x 2 + 2 x 3 = 10 cycles
CPI for sequence 1 = clock cycles / instruction count
i.e average or effective CPI
= 10 /5 = 2
• CPU cycles for sequence 2 = 4 x 1 + 1 x 2 + 1 x 3 = 9 cycles
CPI for sequence 2 = 9 / 6 = 1.5
n
CPU clock cycles  
i 1
CPI  C 
i
i
CPI = CPU Cycles / I
EECC550 - Shaaban
#12 Lec # 3
Winter 2012 12-4-2012
Instruction Frequency & CPI
• Given a program with n types or classes of
instructions with the following characteristics:
i = 1, 2, …. n
Ci = Count of instructions of typei executed
CPIi = Average cycles per instruction of typei
Fi = Frequency or fraction of instruction typei executed
= Ci/ total executed instruction count = Ci/ I
Where: Executed Instruction Count I = S C
Then:
CPI   CPI i  F i 
n
i 1
i.e average or effective CPI
Fraction of total execution time for instructions of type i =
T = I x CPI x C
CPIi x Fi
CPI
EECC550 - Shaaban
#13 Lec # 3
Winter 2012 12-4-2012
i
Instruction Type Frequency & CPI:
A RISC Example
CPIi x Fi
Program Profile or Executed Instructions Mix
Given
Base Machine (Reg / Reg)
Op
Freq, Fi CPIi
ALU
50%
1
Load
20%
5
Store
10%
3
Branch
20%
2
Typical Mix
n
i.e average or effective CPI
CPI
Depends on CPU Design
CPIi x Fi
.5
1.0
.3
.4
% Time
23% = .5/2.2
45% = 1/2.2
14% = .3/2.2
18% = .4/2.2
Sum = 2.2
CPI   CPI i  F i 
i 1
CPI = .5 x 1 + .2 x 5 + .1 x 3 + .2 x 2 = 2.2
= .5 +
1 + .3 + .4
T = I x CPI x C
EECC550 - Shaaban
#14 Lec # 3
Winter 2012 12-4-2012
Metrics of Computer Performance
(Measures)
Execution time: Target workload,
SPEC, etc.
Application
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 purpose, and each can be misused.
EECC550 - Shaaban
#15 Lec # 3
Winter 2012 12-4-2012
Choosing Programs To Evaluate Performance
Levels of programs or benchmarks that could be used to evaluate
performance:
– Actual Target Workload: Full applications that run on the
target machine.
– Real Full Program-based Benchmarks:
• Select a specific mix or suite of programs that are typical of
targeted applications or workload (e.g SPEC95, SPEC CPU2000).
– Small “Kernel” Benchmarks:
Also called synthetic benchmarks
• Key computationally-intensive pieces extracted from real programs.
– Examples: Matrix factorization, FFT, tree search, etc.
• Best used to test specific aspects of the machine.
– Microbenchmarks:
• Small, specially written programs to isolate a specific aspect of
performance characteristics: Processing: integer, floating point,
local memory, input/output, etc.
EECC550 - Shaaban
#16 Lec # 3
Winter 2012 12-4-2012
Types of Benchmarks
Cons
Pros
• Representative
• Portable.
• Widely used.
• Measurements
useful in reality.
Actual Target Workload
Full Application Benchmarks
• Easy to run, early in
the design cycle.
• Identify peak
performance and
potential bottlenecks.
Small “Kernel”
Benchmarks
Microbenchmarks
• Very specific.
• Non-portable.
• Complex: Difficult
to run, or measure.
• Less representative
than actual workload.
• Easy to “fool” by
designing hardware
to run them well.
• Peak performance
results may be a long
way from real application
performance
EECC550 - Shaaban
#17 Lec # 3
Winter 2012 12-4-2012
SPEC: System Performance Evaluation Corporation
The most popular and industry-standard set of CPU benchmarks.
• SPECmarks, 1989:
–
Programs application domain: Engineering and scientific computation
10 programs yielding a single number (“SPECmarks”).
• SPEC92, 1992:
– SPECInt92 (6 integer programs) and SPECfp92 (14 floating point programs).
• SPEC95, 1995:
–
SPECint95 (8 integer programs):
• go, m88ksim, gcc, compress, li, ijpeg, perl, vortex
–
SPECfp95 (10 floating-point intensive programs):
• tomcatv, swim, su2cor, hydro2d, mgrid, applu, turb3d, apsi, fppp, wave5
–
Performance relative to a Sun SuperSpark I (50 MHz) which is given a score of SPECint95
= SPECfp95 = 1
• SPEC CPU2000, 1999:
–
CINT2000 (11 integer programs). CFP2000 (14 floating-point intensive programs)
–
Performance relative to a Sun Ultra5_10 (300 MHz) which is given a score of SPECint2000
= SPECfp2000 = 100
• SPEC CPU2006, 2006:
–
CINT2006 (12 integer programs). CFP2006 (17 floating-point intensive programs)
–
Performance relative to a Sun Ultra Enterprise 2 workstation with a 296-MHz
UltraSPARC II processor which is given a score of SPECint2006 = SPECfp2006 = 1
All based on execution time and give speedup over a reference CPU
EECC550 - Shaaban
#18 Lec # 3
Winter 2012 12-4-2012
SPEC95 Programs
Programs application domain: Engineering and scientific computation
Benchmark
Integer
Floating
Point
go
m88ksim
gcc
compress
li
ijpeg
perl
vortex
tomcatv
swim
su2cor
hydro2d
mgrid
applu
trub3d
apsi
fpppp
wave5
Description
Artificial intelligence; plays the game of Go
Motorola 88k chip simulator; runs test program
The Gnu C compiler generating SPARC code
Compresses and decompresses file in memory
Lisp interpreter
Graphic compression and decompression
Manipulates strings and prime numbers in the special-purpose programming language Perl
A database program
A mesh generation program
Shallow water model with 513 x 513 grid
quantum physics; Monte Carlo simulation
Astrophysics; Hydrodynamic Naiver Stokes equations
Multigrid solver in 3-D potential field
Parabolic/elliptic partial differential equations
Simulates isotropic, homogeneous turbulence in a cube
Solves problems regarding temperature, wind velocity, and distribution of pollutant
Quantum chemistry
Plasma physics; electromagnetic particle simulation
Resulting Performance relative to a Sun SuperSpark I (50 MHz) which is given a score of SPECint95 = SPECfp95 = 1
EECC550 - Shaaban
#19 Lec # 3
Winter 2012 12-4-2012
Sample SPECint95 (Integer) Results
Source URL: http://www.macinfo.de/bench/specmark.html
Sun SuperSpark I (50 MHz) score = 1
T = I x CPI x C
EECC550 - Shaaban
#20 Lec # 3
Winter 2012 12-4-2012
Sample SPECfp95 (Floating Point) Results
Source URL: http://www.macinfo.de/bench/specmark.html
Sun SuperSpark I (50 MHz) score = 1
T = I x CPI x C
EECC550 - Shaaban
#21 Lec # 3
Winter 2012 12-4-2012
SPEC CPU2000 Programs
CINT2000
(Integer)
11 programs
CFP2000
(Floating
Point)
14 programs
Benchmark
Language
Descriptions
164.gzip
175.vpr
176.gcc
181.mcf
186.crafty
197.parser
252.eon
253.perlbmk
254.gap
255.vortex
256.bzip2
300.twolf
C
C
C
C
C
C
C++
C
C
C
C
C
Compression
FPGA Circuit Placement and Routing
C Programming Language Compiler
Combinatorial Optimization
Game Playing: Chess
Word Processing
Computer Visualization
PERL Programming Language
Group Theory, Interpreter
Object-oriented Database
Compression
Place and Route Simulator
168.wupwise
171.swim
172.mgrid
173.applu
177.mesa
178.galgel
179.art
183.equake
187.facerec
188.ammp
189.lucas
191.fma3d
200.sixtrack
301.apsi
Fortran 77
Fortran 77
Fortran 77
Fortran 77
C
Fortran 90
C
C
Fortran 90
C
Fortran 90
Fortran 90
Fortran 77
Fortran 77
Physics / Quantum Chromodynamics
Shallow Water Modeling
Multi-grid Solver: 3D Potential Field
Parabolic / Elliptic Partial Differential Equations
3-D Graphics Library
Computational Fluid Dynamics
Image Recognition / Neural Networks
Seismic Wave Propagation Simulation
Image Processing: Face Recognition
Computational Chemistry
Number Theory / Primality Testing
Finite-element Crash Simulation
High Energy Nuclear Physics Accelerator Design
Meteorology: Pollutant Distribution
Programs application domain: Engineering and scientific computation
Source: http://www.spec.org/cpu2000/
EECC550 - Shaaban
#22 Lec # 3
Winter 2012 12-4-2012
Integer SPEC CPU2000 Microprocessor
Performance 1978-2006
Performance relative to VAX 11/780 (given a score = 1)
EECC550 - Shaaban
#23 Lec # 3
Winter 2012 12-4-2012
Top 20 SPEC CPU2000 Results (As of March 2002)
Top 20 SPECint2000
#
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
MHz
1300
2200
2200
1667
1000
1400
1050
1533
750
833
1400
833
600
675
900
552
750
700
800
400
Processor
POWER4
Pentium 4
Pentium 4 Xeon
Athlon XP
Alpha 21264C
Pentium III
UltraSPARC-III Cu
Athlon MP
PA-RISC 8700
Alpha 21264B
Athlon
Alpha 21264A
MIPS R14000
SPARC64 GP
UltraSPARC-III
PA-RISC 8600
POWER RS64-IV
Pentium III Xeon
Itanium
MIPS R12000
int peak
814
811
810
724
679
664
610
609
604
571
554
533
500
478
467
441
439
438
365
353
Top 20 SPECfp2000
int base
790
790
788
697
621
648
537
587
568
497
495
511
483
449
438
417
409
431
358
328
MHz
1300
1000
1050
2200
2200
833
800
833
1667
750
1533
600
675
900
1400
1400
500
450
500
400
Processor
POWER4
Alpha 21264C
UltraSPARC-III Cu
Pentium 4 Xeon
Pentium 4
Alpha 21264B
Itanium
Alpha 21264A
Athlon XP
PA-RISC 8700
Athlon MP
MIPS R14000
SPARC64 GP
UltraSPARC-III
Athlon
Pentium III
PA-RISC 8600
POWER3-II
Alpha 21264
MIPS R12000
Performance relative to a Sun Ultra5_10 (300 MHz) which is given a score of SPECint2000 = SPECfp2000 = 100
Source: http://www.aceshardware.com/SPECmine/top.jsp
fp peak
1169
960
827
802
801
784
701
644
642
581
547
529
509
482
458
456
440
433
422
407
fp base
1098
776
701
779
779
643
701
571
596
526
504
499
371
427
426
437
397
426
383
382
EECC550 - Shaaban
#24 Lec # 3
Winter 2012 12-4-2012
Top 20 SPEC CPU2000 Results (As of October 2006)
Top 20 SPECint2000
# MHz Processor
int peak
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
2933
3000
2666
2660
3000
2800
2800
2300
3733
3800
2260
3600
2167
3600
3466
2700
2600
2000
2160
1600
Core 2 Duo EE
Xeon 51xx
Core 2 Duo
Xeon 30xx
Opteron
Athlon 64 FX
Opteron AM2
POWER5+
Pentium 4 E
Pentium 4 Xeon
Pentium M
Pentium D
Core Duo
Pentium 4
Pentium 4 EE
PowerPC 970MP
Athlon 64
Pentium 4 Xeon LV
SPARC64 V
Itanium 2
3119
3102
2848
2835
2119
2061
1960
1900
1872
1856
1839
1814
1804
1774
1772
1706
1706
1668
1620
1590
int base
3108
3089
2844
2826
1942
1923
1749
1820
1870
1854
1812
1810
1796
1772
1701
1623
1612
1663
1501
1590
Top 20 SPECfp2000
MHz Processor
fp peak fp base
2300
1600
3000
2933
2660
1600
2667
1900
3000
2800
3733
2800
2700
2160
3730
3600
3600
2600
1700
3466
Performance relative to a Sun Ultra5_10 (300 MHz) which is given a score of SPECint2000 = SPECfp2000 = 100
Source: http://www.aceshardware.com/SPECmine/top.jsp
POWER5+
DC Itanium 2
Xeon 51xx
Core 2 Duo EE
Xeon 30xx
Itanium 2
Core 2 Duo
POWER5
Opteron
Opteron AM2
Pentium 4 E
Athlon 64 FX
PowerPC 970MP
SPARC64 V
Pentium 4 Xeon
Pentium D
Pentium 4
Athlon 64
POWER4+
Pentium 4 EE
3642
3098
3056
3050
3044
3017
2850
2796
2497
2462
2283
2261
2259
2236
2150
2077
2015
1829
1776
1724
3369
3098
2811
3048
2763
3017
2847
2585
2260
2230
2280
2086
2060
2094
2063
2073
2009
1700
1642
1719
EECC550 - Shaaban
#25 Lec # 3
Winter 2012 12-4-2012
SPEC CPU2006 Programs
CINT2006
(Integer)
12 programs
CFP2006
(Floating
Point)
17 programs
Benchmark
Language
Descriptions
400.perlbench
401.bzip2
403.gcc
429.mcf
445.gobmk
456.hmmer
458.sjeng
462.libquantum
464.h264ref
471.omnetpp
473.astar
483.Xalancbmk
410.bwaves
416.gamess
433.milc
434.zeusmp
435.gromacs
436.cactusADM
437.leslie3d
444.namd
447.dealII
450.soplex
453.povray
454.calculix
459.GemsFDTD
465.tonto
470.lbm
481.wrf
482.sphinx3
C
C
C
C
C
C
C
C
C
C++
C++
C++
Fortran
Fortran
C
Fortran
C/Fortran
C/Fortran
Fortran
C++
C++
C++
C++
C/Fortran
Fortran
Fortran
C
C/Fortran
C
PERL Programming Language
Compression
C Compiler
Combinatorial Optimization
Artificial Intelligence: go
Search Gene Sequence
Artificial Intelligence: chess
Physics: Quantum Computing
Video Compression
Discrete Event Simulation
Path-finding Algorithms
XML Processing
Fluid Dynamics
Quantum Chemistry
Physics: Quantum Chromodynamics
Physics/CFD
Biochemistry/Molecular Dynamics
Physics/General Relativity
Fluid Dynamics
Biology/Molecular Dynamics
Finite Element Analysis
Linear Programming, Optimization
Image Ray-tracing
Structural Mechanics
Computational Electromagnetics
Quantum Chemistry
Fluid Dynamics
Weather Prediction
Speech recognition
Programs application domain: Engineering and scientific computation
Source: http://www.spec.org/cpu2006/
EECC550 - Shaaban
#26 Lec # 3
Winter 2012 12-4-2012
Example Integer SPEC CPU2006 Performance Results
For 2.5 GHz AMD Opteron X4 model 2356 (Barcelona)
Score
Average
I
CPI
C
Performance relative to Base Processor a 296-MHz UltraSPARC II
which is given a score of SPECint2006 = SPECfp2006 = 1
(speedup)
T
T on base processor
EECC550 - Shaaban
#27 Lec # 3
Winter 2012 12-4-2012
Computer Performance Measures :
MIPS (Million Instructions Per Second) Rating
•
For a specific program running on a specific CPU the MIPS rating is a measure
of how many millions of instructions are executed per second:
MIPS Rating = Instruction count / (Execution Time x 106)
= Instruction count / (CPU clocks x Cycle time x 106)
= (Instruction count x Clock rate) / (Instruction count x CPI x 106)
= Clock rate / (CPI x 106)
•
Major problem with MIPS rating: As shown above the MIPS rating does not account for
the count of instructions executed (I).
– A higher MIPS rating in many cases may not mean higher performance or
better execution time. i.e. due to compiler design variations.
• In addition the MIPS rating:
– Does not account for the instruction set architecture (ISA) used.
• Thus it cannot be used to compare computers/CPUs with different instruction
sets.
– Easy to abuse: Program used to get the MIPS rating is often omitted.
• Often the Peak MIPS rating is provided for a given CPU which is obtained using
a program comprised entirely of instructions with the lowest CPI for the given
CPU design which does not represent real programs.
T = I x CPI x C
EECC550 - Shaaban
#28 Lec # 3
Winter 2012 12-4-2012
Computer Performance Measures :
MIPS (Million Instructions Per Second) Rating
• Under what conditions can the MIPS rating be used to
compare performance of different CPUs?
• The MIPS rating is only valid to compare the performance of
different CPUs provided that the following conditions are satisfied:
1 The same program is used
(actually this applies to all performance metrics)
2 The same ISA is used
3 The same compiler is used
 (Thus the resulting programs used to run on the CPUs and
obtain the MIPS rating are identical at the machine code
(binary)
level including the same instruction count)
EECC550 - Shaaban
#29 Lec # 3
Winter 2012 12-4-2012
Compiler Variations, MIPS & Performance:
An Example
• For a machine (CPU) with instruction classes:
e.g ALU, Branch etc.
Instruction class
A
B
C
CPI
1
2
3
For a specific
CPU design
• For a given high-level language program, two compilers
produced the following executed instruction counts:
Code from:
Compiler 1
Compiler 2
Instruction counts (in millions)
for each instruction class
A
B
C
5
1
1
10
1
1
• The machine is assumed to run at a clock rate of 100 MHz.
EECC550 - Shaaban
#30 Lec # 3
Winter 2012 12-4-2012
Compiler Variations, MIPS & Performance:
An Example (Continued)
MIPS = Clock rate / (CPI x 106) = 100 MHz / (CPI x 106)
CPI = CPU execution cycles
/ Instructions count
n
CPU clock cycles  
i 1
CPI  C 
i
i
CPU time = Instruction count x CPI / Clock rate
•
For compiler 1:
– CPI1 = (5 x 1 + 1 x 2 + 1 x 3) / (5 + 1 + 1) = 10 / 7 = 1.43
– MIPS Rating1 = 100 / (1.428 x 106) = 70.0 MIPS
– CPU time1 = ((5 + 1 + 1) x 106 x 1.43) / (100 x 106) = 0.10 seconds
•
For compiler 2:
– CPI2 = (10 x 1 + 1 x 2 + 1 x 3) / (10 + 1 + 1) = 15 / 12 = 1.25
– MIPS Rating2 = 100 / (1.25 x 106) = 80.0 MIPS
– CPU time2 = ((10 + 1 + 1) x 106 x 1.25) / (100 x 106) = 0.15 seconds
MIPS rating indicates that compiler 2 is better
while in reality the code produced by compiler 1 is faster
EECC550 - Shaaban
#31 Lec # 3
Winter 2012 12-4-2012
MIPS (The ISA not the metric) Loop Performance Example
High Memory
$6 points here
For the loop:
X[999]
X[998]
Last element to
compute
.
.
.
.
for (i=0; i<1000; i=i+1){
x[i] = x[i] + s; }
$2 initially
MIPS assembly code is given by:
loop:
lw
addi
lw
add
sw
addi
bne
$3,
$6,
$4,
$5,
$5,
$2,
$6,
0($1)
$2, 4000
0($2)
$4, $3
0($2)
$2, 4
$2, loop
points here
;
;
;
;
;
;
;
X[0]
Low Memory
First element to
compute
load s in $3
$6 = address of last element + 4
load x[i] in $4
$5 has x[i] + s
store computed x[i]
increment $2 to point to next x[ ] element
last loop iteration reached?
The MIPS code is executed on a specific CPU that runs at 500 MHz (C = clock cycle = 2ns = 2x10 -9 seconds)
with following instruction type CPIs :
For this MIPS code running on this CPU find:
Instruction type
ALU
Load
Store
Branch
CPI
4
5
7
3
1- Fraction of total instructions executed for each instruction type
2- Total number of CPU cycles
3- Average CPI
4- Fraction of total execution time for each instructions type
5- Execution time
6- MIPS rating , peak MIPS rating for this CPU
X[ ] array of words in memory, base address in $2 ,
s a constant word value in memory, address in $1
EECC550 - Shaaban
#32 Lec # 3
Winter 2012 12-4-2012
MIPS (The ISA) Loop Performance Example (continued)
•
•
The code has 2 instructions before the loop and 5 instructions in the body of the loop which iterates 1000
times,
Thus: Total instructions executed, I = 5x1000 + 2 = 5002 instructions
1
Number of instructions executed/fraction Fi for each instruction type:
–
–
–
–
2
ALU instructions = 1 + 2x1000 = 2001
Load instructions = 1 + 1x1000 = 1001
Store instructions = 1000
Branch instructions = 1000
CPU clock cycles 
 CPI
n
i 1
3
4
CPIALU = 4
FractionALU = FALU = 2001/5002 = 0.4 = 40%
CPILoad = 5
FractionLoad = FLoad = 1001/5002= 0.2 = 20%
CPIStore = 7 FractionStore = FStore = 1000/5002 = 0.2 = 20%
CPIBranch = 3 FractionBranch= FBranch = 1000/5002= 0.2 = 20%
i
 Ci

= 2001x4 + 1001x5 + 1000x7 + 1000x3 = 23009 cycles
Average CPI = CPU clock cycles / I = 23009/5002 = 4.6
Instruction type
Fraction of execution time for each instruction type:
–
–
–
–
ALU
Load
Store
Branch
Fraction of time for ALU instructions = CPIALU x FALU / CPI= 4x0.4/4.6 = 0.348 = 34.8%
Fraction of time for load instructions = CPIload x Fload / CPI= 5x0.2/4.6 = 0.217 = 21.7%
Fraction of time for store instructions = CPIstore x Fstore / CPI= 7x0.2/4.6 = 0.304 = 30.4%
Fraction of time for branch instructions = CPIbranch x Fbranch / CPI= 3x0.2/4.6 = 0.13 = 13%
5
Execution time = I x CPI x C = CPU cycles x C = 23009 x 2x10-9 =
= 4.6x 10-5 seconds = 0.046 msec = 46 usec
6
MIPS rating = Clock rate / (CPI x 106) = 500 / 4.6 = 108.7 MIPS
–
–
CPI
The CPU achieves its peak MIPS rating when executing a program that only has
instructions of the type with the lowest CPI. In this case branches with CPI Branch = 3
Peak MIPS rating = Clock rate / (CPIBranch x 106) = 500/3 = 166.67 MIPS
EECC550 - Shaaban
#33 Lec # 3
Winter 2012 12-4-2012
4
5
7
3
Computer Performance Measures :
MFLOPS (Million FLOating-Point Operations Per Second)
•
•
A floating-point operation is an addition, subtraction, multiplication, or division
operation applied to numbers represented by a single or a double precision
floating-point representation.
MFLOPS, for a specific program running on a specific computer, is a measure
of millions of floating point-operation (megaflops) per second:
MFLOPS = Number of floating-point operations / (Execution time x 106 )
•
•
•
MFLOPS rating is a better comparison measure between different machines
(applies even if ISAs are different) than the MIPS rating.
– Applicable even if ISAs are different
Program-dependent: Different programs have different percentages of
floating-point operations present. i.e compilers have no floating- point
operations and yield a MFLOPS rating of zero.
Dependent on the type of floating-point operations present in the program.
– Peak MFLOPS rating for a CPU: Obtained using a program comprised
entirely of the simplest floating point instructions (with the lowest CPI) for
the given CPU design which does not represent real floating point programs.
Current peak MFLOPS rating: 8,000-20,000
MFLOPS (8-20 GFLOPS) per processor core
EECC550 - Shaaban
#34 Lec # 3
Winter 2012 12-4-2012
Quantitative Principles
of Computer Design
• Amdahl’s Law:
The performance gain from improving some portion of
a computer is calculated by:
i.e using some enhancement
Speedup =
Performance for entire task using the enhancement
Performance for the entire task without using the enhancement
Before Enhancement
or Speedup =
Execution time without the enhancement
Execution time for entire task using the enhancement
After Enhancement
Here: Task = Program
4th Edition: Chapter 1.8
Recall: Performance = 1 /Execution Time
3rd Edition: Chapter 4.5
EECC550 - Shaaban
#35 Lec # 3
Winter 2012 12-4-2012
Performance Enhancement Calculations:
Amdahl's Law
• The performance enhancement possible due to a given design
improvement is limited by the amount that the improved feature is used
• Amdahl’s Law:
Performance improvement or speedup due to enhancement E:
Execution Time without E
Speedup(E) = -------------------------------------Execution Time with E
original
Performance with E
= --------------------------------Performance without E
– Suppose that enhancement E accelerates a fraction F of the
execution time by a factor S and the remainder of the time is
unaffected then:
Execution Time with E = ((1-F) + F/S) X Execution Time without E
Hence speedup is given by:
Execution Time without E
1
Speedup(E) = --------------------------------------------------------- = -------------------((1 - F) + F/S) X Execution Time without E
(1 - F) + F/S
F (Fraction of execution time enhanced) refers
to original execution time before the enhancement is applied
EECC550 - Shaaban
#36 Lec # 3
Winter 2012 12-4-2012
Pictorial Depiction of Amdahl’s Law
Enhancement E accelerates fraction F of original execution time by a factor of S
Before:
Execution Time without enhancement E: (Before enhancement is applied)
• shown normalized to 1 = (1-F) + F =1
Unaffected fraction: (1- F)
Affected fraction: F
Unchanged
Unaffected fraction: (1- F)
After:
Execution Time with enhancement E:
F/S
What if the fraction given is
after the enhancement has been applied?
How would you solve the problem?
(i.e find expression for speedup)
Execution Time without enhancement E
1
Speedup(E) = ------------------------------------------------------ = -----------------Execution Time with enhancement E
(1 - F) + F/S
EECC550 - Shaaban
#37 Lec # 3
Winter 2012 12-4-2012
Performance Enhancement Example
• For the RISC machine with the following instruction mix given earlier:
Op
ALU
Load
Store
Freq
50%
20%
10%
Cycles
1
5
3
CPI(i)
.5
1.0
.3
% Time
23%
45%
14%
CPI = 2.2
From a previous example
Branch
20%
2
.4
18%
• If a CPU design enhancement improves the CPI of load instructions
from 5 to 2, what is the resulting performance improvement from this
enhancement:
Fraction enhanced = F = 45% or .45
Unaffected fraction = 1- F = 100% - 45% = 55% or .55
Factor of enhancement = S = 5/2 = 2.5
Using Amdahl’s Law:
1
1
Speedup(E) = ------------------ = --------------------- =
(1 - F) + F/S
.55 + .45/2.5
1.37
EECC550 - Shaaban
#38 Lec # 3
Winter 2012 12-4-2012
An Alternative Solution Using CPU Equation
Op
ALU
Load
Store
Freq
50%
20%
10%
Cycles
1
5
3
CPI(i)
.5
1.0
.3
% Time
23%
45%
14%
CPI = 2.2
Branch
20%
2
.4
18%
• If a CPU design enhancement improves the CPI of load instructions
from 5 to 2, what is the resulting performance improvement from this
enhancement:
New CPI of load is now 2 instead of 5
Old CPI = 2.2
New CPI = .5 x 1 + .2 x 2 + .1 x 3 + .2 x 2 = 1.6
Original Execution Time
Speedup(E) = ----------------------------------New Execution Time
Instruction count x old CPI x clock cycle
= ---------------------------------------------------------------Instruction count x new CPI x clock cycle
old CPI
= ------------ =
new CPI
2.2
--------1.6
= 1.37
Which is the same speedup obtained from Amdahl’s Law in the first solution.
T = I x CPI x C
EECC550 - Shaaban
#39 Lec # 3
Winter 2012 12-4-2012
Performance Enhancement Example
• A program runs in 100 seconds on a machine with multiply
operations responsible for 80 seconds of this time. By how much
must the speed of multiplication be improved to make the program
four times faster?
Desired speedup = 4 =



100
----------------------------------------------------Execution Time with enhancement
Execution time with enhancement = 100/4 = 25 seconds
25 seconds = (100 - 80 seconds) + 80 seconds / S
25 seconds =
20 seconds
+ 80 seconds / S
5 = 80 seconds / S
S = 80/5 = 16
Alternatively, it can also be solved by finding enhanced fraction of execution time:
F = 80/100 = .8
and then solving Amdahl’s speedup equation for desired enhancement factor S
1
Speedup(E) = ------------------ = 4 =
(1 - F) + F/S
1
1
----------------- = --------------(1 - .8) + .8/S
.2 + .8/s
Hence multiplication should be 16 times
faster to get an overall speedup of 4.
Machine = CPU
Solving for S gives S= 16
EECC550 - Shaaban
#40 Lec # 3
Winter 2012 12-4-2012
Performance Enhancement Example
• For the previous example with a program running in 100 seconds on
a machine with multiply operations responsible for 80 seconds of this
time. By how much must the speed of multiplication be improved
to make the program five times faster?
Desired speedup = 5 =

100
----------------------------------------------------Execution Time with enhancement
Execution time with enhancement = 100/5 = 20 seconds
20 seconds = (100 - 80 seconds) + 80 seconds / s
20 seconds =
20 seconds
+ 80 seconds / s

0 = 80 seconds / s
No amount of multiplication speed improvement can achieve this.
EECC550 - Shaaban
#41 Lec # 3
Winter 2012 12-4-2012
Extending Amdahl's Law To Multiple Enhancements
n enhancements each affecting a different portion of execution time
• Suppose that enhancement Ei accelerates a fraction Fi of the
original execution time by a factor Si and the remainder of the
time is unaffected then:
i = 1, 2, …. n
Speedup 
Original Execution Time
((1   F )   F ) XOriginal
i
i
i
i
S
Execution Time
i
Unaffected fraction
Speedup 
1
((1   F )   F )
i
i
i
i
S
What if the fractions given are
after the enhancements were applied?
How would you solve the problem?
(i.e find expression for speedup)
i
Note: All fractions Fi refer to original execution time before the
enhancements are applied.
EECC550 - Shaaban
#42 Lec # 3
Winter 2012 12-4-2012
Amdahl's Law With Multiple Enhancements:
Example
•
Three CPU performance enhancements are proposed with the following
speedups and percentage of the code original execution time affected:
Speedup1 = S1 = 10
Speedup2 = S2 = 15
Speedup3 = S3 = 30
•
•
Percentage1 = F1 = 20%
Percentage1 = F2 = 15%
Percentage1 = F3 = 10%
While all three enhancements are in place in the new design, each
enhancement affects a different portion of the code and only one
enhancement can be used at a time.
What is the resulting overall speedup?
Speedup 
1
((1   F )   F )
i
i
•
i
i
S
i
Speedup = 1 / [(1 - .2 - .15 - .1) + .2/10 + .15/15 + .1/30)]
= 1/ [
.55
+
.0333
]
= 1 / .5833 = 1.71
EECC550 - Shaaban
#43 Lec # 3
Winter 2012 12-4-2012
Pictorial Depiction of Example
Before:
Execution Time with no enhancements: 1
Unaffected, fraction: .55
i.e normalized to 1
S1 = 10
F1 = .2
S2 = 15
S3 = 30
F2 = .15
F3 = .1
/ 15
/ 10
/ 30
Unchanged
Unaffected, fraction: .55
After:
Execution Time with enhancements: .55 + .02 + .01 + .00333 = .5833
What if the fractions given are
after the enhancements were applied?
How would you solve the problem?
Speedup = 1 / .5833 = 1.71
Note: All fractions Fi refer to original execution time.
EECC550 - Shaaban
#44 Lec # 3
Winter 2012 12-4-2012
“Reverse” Multiple Enhancements Amdahl's Law
•
•
Multiple Enhancements Amdahl's Law assumes that the fractions given
refer to original execution time.
If for each enhancement Si the fraction Fi it affects is given as a fraction
of the resulting execution time after the enhancements were applied
then:
(
(1   F )   F  S ) XResulting
Speedup 
i
i
i
i
Execution Time
Resulting Execution Time
Unaffected fraction
Speedup 
i
(1  i F i)  i F i  S i
1
 (1  i F i )  i F i  S i
i.e as if resulting execution time is normalized to 1
•
For the previous example assuming fractions given refer to resulting
execution time after the enhancements were applied (not the original
execution time), then:
Speedup = (1 - .2 - .15 - .1) + .2 x10 + .15 x15 + .1x30
=
.55
+ 2
+ 2.25 + 3
= 7.8
Find original fractions?
EECC550 - Shaaban
#45 Lec # 3
Winter 2012 12-4-2012