Advanced Computing Techniques &

Applications

Dr. Bo Yuan

E-mail: yuanb@sz.tsinghua.edu.cn

4

Course Profile

• Lecturer: Dr. Bo Yuan

• Contact– Phone: 2603 6067– E-mail: yuanb@sz.tsinghua.edu.cn– Room: F-301B

• Time: 10:25 am – 12:00pm, Friday

• Venue: CI-107 & B-204 (Lab)

• Teaching Assistant– Mr. Pengtao Huang– hpt13@mails.tsinghua.edu.cn

5

We will study ...• MPI

– Message Passing Interface– API for distributed memory parallel computing (multiple processes)– The dominant model used in cluster computing

• OpenMP– Open Multi-Processing– API for shared memory parallel computing (multiple threads)

• GPU Computing with CUDA– Graphics Processing Unit– Compute Unified Device Architecture– API for shared memory parallel computing in C (multiple threads)

• Parallel Matlab– A popular high-level technical computing language and interactive environment

6

Aims & Objectives

• Learning Objectives– Understand the main issues and core techniques in parallel computing.

– Able to develop MPI based parallel programs.

– Able to develop OpenMP based parallel programs.

– Able to develop GPU based parallel programs.

– Able to develop Matlab based parallel programs.

• Graduate Attributes– In-depth Knowledge of the Field of Study

– Effective Communication

– Independence and Teamwork

– Critical Judgment

7

Learning Activities• Lecture (9)

– Introduction (3)– MPI and OpenMP (3)– GPU Computing (3)

• Practice (4)– MPI (1)– OpenMP (1)– GPU Programming (1)– Parallel Matlab (1)

• Others (3)– Industry Tour (1)– Presentation (1)– Final Exam (1)

8

Learning Resources

9

Learning Resources• Books

– http://www.mcs.anl.gov/~itf/dbpp/– https://computing.llnl.gov/tutorials/parallel_comp/– http://www-users.cs.umn.edu/~karypis/parbook/

• Journals– http://www.computer.org/tpds– http://www.journals.elsevier.com/parallel-computing/– http://www.journals.elsevier.com/journal-of-parallel-and-distributed-computing/

• Amazon Cloud Computing Services– http://aws.amazon.com

• CUDA– http://developer.nvidia.com

10

Learning Resources

https://www.coursera.org/course/hetero

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Assessment

20% 40% 40%

12

Group Project

https://developer.nvidia.com/embedded-computing

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Rules & Policies• Plagiarism– Plagiarism is the act of misrepresenting as one's own original work the ideas,

interpretations, words or creative works of another.

– Direct copying of paragraphs, sentences, a single sentence or significant parts of a sentence.

– Presenting as independent work done in collaboration with others.

– Copying ideas, concepts, research results, computer codes, statistical tables, designs, images, sounds or text or any combination of these.

– Paraphrasing, summarizing or simply rearranging another person's words, ideas, without changing the basic structure and/or meaning of the text.

– Copying or adapting another student's original work into a submitted assessment item.

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Rules & Policies

• Late Submission– Late submissions will incur a penalty of 10% of the total marks for each day that the

submission is late (including weekends). Submissions more than 5 days late will not be accepted.

• Assumed Background– Acquaintance with C language is essential.– Knowledge of computer architecture is beneficial.

• We have CUDA supported GPU cards available!

15

Half Adder

A: Augend B: Addend

S: Sum C: Carry

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Full Adder

17

SR Latch

S R Q0 0 Q

0 1 0

1 0 1

1 1 N/A

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Address Decoder

19

Address Decoder

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Electronic Numerical Integrator And Computer

• Speed (10-digit decimal numbers)– Machine Cycle: 5000 cycles per second– Multiplication: 357 times per second– Division/Square Root: 35 times per second

• Programming– Programmable– Switches and Cables– Usually took days.– I/O: Punched Cards

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Stored-Program Computer

22

Personal Computer in 1980s

BASIC IBM PC/AT

23

24

25

Top 500 SupercomputersG

FLO

PS

26

Cost of ComputingDate Approximate cost per GFLOPS Approximate cost per GFLOPS

inflation adjusted to 2013 dollars

1984 $15,000,000 $33,000,0001997 $30,000 $42,000April 2000 $1,000 $1,300May 2000 $640 $836August 2003 $82 $100August 2007 $48 $52March 2011 $1.80 $1.80August 2012 $0.75 $0.73December 2013 $0.12 $0.12

27

Complexity of Computing

• A: 10×100 B: 100×5 C: 5×50

• (AB)C vs. A(BC)

• A: N×N B: N×N C=AB

• Time Complexity: O(N3)

• Space Complexity: O(1)

28

Why Parallel Computing?

• Why we need every-increasing performance:– Big Data Analysis– Climate Modeling– Gaming

• Why we need to build parallel systems:– Increase the speed of integrated circuits Overheating– Increase the number of transistors Multi-Core

• Why we need to learn parallel programming:– Running multiple instances of the same program is unlikely to help.– Need to rewrite serial programs to make them parallel.

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Parallel Sum1, 4, 3 9, 2, 8 5, 1, 1 6, 2, 7 2, 5, 0 4, 1, 8 6, 5 ,1 2, 3, 9

0 1 2 76543 Cores

8 19 7 15 7 13 12 14

0 95

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Parallel Sum1, 4, 3 9, 2, 8 5, 1, 1 6, 2, 7 2, 5, 0 4, 1, 8 6, 5 ,1 2, 3, 9

0 1 2 76543 Cores

8 19 7 15 7 13 12 14

0 2 4 627 22 20 26

95

0 4

0

49 46

31

Prefix Scan

3 5 2 5 7 9 4 6

3 8 10 15 22 31 35 41

0 3 8 10 15 22 31 35

Original Vector

Inclusive Prefix Scan

Exclusive Prefix Scan

prefixScan[0]=A[0];for (i=1; i<N; i++) prefixScan[i]=prfixScan[i-1]+A[i];

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Parallel Prefix Scan3 5 2 5 7 9 -4 6 7 -3 1 7 6 8 -1 2

3 5 2 5 7 9 -4 6 7 -3 1 7 6 8 -1 2

3 8 10 15 7 16 12 18 7 4 5 12 6 14 13 15

15 18 12 15

0 15 33 45

3 8 10 15 22 31 27 33 40 37 38 45 51 59 58 60

Exclusive Prefix Scan

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Levels of Parallelism

• Embarrassingly Parallel– No dependency or communication between parallel tasks

• Coarse-Grained Parallelism– Infrequent communication, large amounts of computation

• Fine-Grained Parallelism– Frequent communication, small amounts of computation– Greater potential for parallelism– More overhead

• Not Parallel– Giving life to a baby takes 9 months.– Can this be done in 1 month by having 9 women?

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Data Decomposition

2 Cores

35

Granularity

8 Cores

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Coordination

• Communication– Sending partial results to other cores

• Load Balancing– Wooden Barrel Principle

• Synchronization– Race Condition

Thread A Thread B1A: Read variable V 1B: Read variable V2A: Add 1 to variable V 2B: Add 1 to variable V3A Write back to variable V 3B: Write back to variable V

37

Data Dependency

• Bernstein's Conditions

• Examples

1: function Dep(a, b) 2: c = a·b 3: d = 3·c 4: end function

1: function NoDep(a, b)2: c = a·b 3: d = 3·b 4: e = a+b 5: end function

ji

ji

ij

OO

OI

OI

Flow Dependency

Output Dependency

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What is not parallel?Recurrences

for (i=1; i<N; i++) a[i]=a[i-1]+b[i];

Loop-Carried Dependence

for (k=5; k<N; k++) { b[k]=DoSomething(K); a[k]=b[k-5]+MoreStuff(k);}

Atypical Loop-Carried Dependence

wrap=a[0]*b[0];for (i=1; i<N; i++) { c[i]=wrap; wrap=a[i]*b[i]; d[i]=2*wrap;}

Solution

for (i=1; i<N; i++) { wrap=a[i-1]*b[i-1]; c[i]=wrap; wrap=a[i]*b[i]; d[i]=2*wrap;}

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What is not parallel?

Induction Variables

i1=4;i2=0;for (k=1; k<N; k++) { B[i1++]=function1(k,q,r); i2+=k; A[i2]=function2(k,r,q);}

Solution

i1=4;i2=0;for (k=1; k<N; k++) { B[k+3]=function1(k,q,r); i2=(k*k+k)/2; A[i2]=function2(k,r,q);}

40

Types of Parallelism

• Instruction Level Parallelism

• Task Parallelism– Different tasks on the same/different sets of data

• Data Parallelism– Similar tasks on different sets of the data

• Example– 5 TAs, 100 exam papers, 5 questions– How to make it task parallel?– How to make it data parallel?

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Assembly Line

15 20 5

• How long does it take to produce a single car?

• How many cars can be operated at the same time?

• How long is the gap between producing the first and the second car?

• The longest stage on the assembly line determines the throughput.

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Instruction Pipeline

IF: Instruction fetch

ID: Instruction decode and register fetch

EX: Execute

MEM: Memory access

WB: Register write back

1: Add 1 to R5.

2: Copy R5 to R6.

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Superscalar

44

Computing Models• Concurrent Computing

– Multiple tasks can be in progress at any instant.

• Parallel Computing– Multiple tasks can be run simultaneously.

• Distributed Computing– Multiple programs on networked computers work collaboratively.

• Cluster Computing– Homogenous, Dedicated, Centralized

• Grid Computing– Heterogonous, Loosely Coupled, Autonomous, Geographically Distributed

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Concurrent vs. Parallel

Core

Job 1 Job 2

Core 1 Core 2

Job 1 Job 2

Core 1 Core 2

Job 3 Job 4Job 1 Job 2

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Process & Thread• Process

– An instance of a computer program being executed

• Threads– The smallest units of processing scheduled by OS– Exist as a subset of a process.– Share the same resources from the process.– Switching between threads is much faster than switching between processes.

• Multithreading– Better use of computing resources– Concurrent execution– Makes the application more responsive

ProcessThread

Thread

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Parallel Processes

Program

Process 1

Process 2

Process 3

Node 1

Node 2

Node 3

Single Program, Multiple Data

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Parallel Threads

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Graphics Processing Unit

50

CPU vs. GPU

51

CUDA

52

CUDA

53

GPU Computing Showcase

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MapReduce vs. GPU• Pros:

– Run on clusters of hundreds or thousands of commodity computers.

– Can handle excessive amount of data with fault tolerance.

– Minimum efforts required for programmers: Map & Reduce

• Cons:– Intermediate results are stored in disks and transferred via network links.

– Suitable for processing independent or loosely coupled jobs.

– High upfront hardware cost and operational cost

– Low Efficiency: GFLOPS per Watt, GFLOPS per Dollar

55

Parallel Computing in Matlab

for i=1:1024 A(i) = sin(i*2*pi/1024); end plot(A);

matlabpool open local 3

parfor i=1:1024 A(i) = sin(i*2*pi/1024); end plot(A);

matlabpool close

56

GPU Computing in Matlab

http://www.mathworks.cn/discovery/matlab-gpu.html

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Cloud Computing

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Everything is Cloud …

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Five Attributes of Cloud Computing• Service Based– What the service needs to do is more important than how the technologies are used to

implement the solution.

• Scalable and Elastic– The service can scale capacity up or down as the consumer demands at the speed of full

automation.

• Shared– Services share a pool of resources to build economies of scale.

• Metered by Use– Services are tracked with usage metrics to enable multiple payment models.

• Uses Internet Technologies– The service is delivered using Internet identifiers, formats and protocols.

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Flynn’s Taxonomy

• Single Instruction, Single Data (SISD)– von Neumann System

• Single Instruction, Multiple Data (SIMD)– Vector Processors, GPU

• Multiple Instruction, Single Data (MISD)– Generally used for fault tolerance

• Multiple Instruction, Multiple Data (MIMD)– Distributed Systems– Single Program, Multiple Data (SPMD)– Multiple Program, Multiple Data (MPMD)

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Flynn’s Taxonomy

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Von Neumann Architecture

Harvard Architecture

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Inside a PC ...

Front-Side Bus (Core 2 Extreme)

8B × 400MHZ × 4/Cycle = 12.8GB/S

Memory (DDR3-1600)

8B × 200MHZ × 4 × 2/Cycle = 12.8GB/S

PCI Express 3.0 (×16)

1GB/S × 16= 16GB/S

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Shared Memory System

CPU CPU CPU CPU

Interconnect

Memory

. . .

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Non-Uniform Memory Access

Core 1 Core 2

Interconnect

Memory

Core 1 Core 2Remote Access

Local Access Local Access

Interconnect

Memory

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Distributed Memory System

CPU

Memory

Communication Networks

CPU

Memory

CPU

Memory

. . .

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Crossbar Switch

P1 P2 P3 P4

M4

M3

M2

M1

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Cache

• Component that transparently stores data so that future requests for that data can be served faster

– Compared to main memory: smaller, faster, more expensive– Spatial Locality– Temporal Locality

• Cache Line– A block of data that is accessed together

• Cache Miss– Failed attempts to read or write a piece of data in the cache– Main memory access required– Read Miss, Write Miss– Compulsory Miss, Capacity Miss, Conflict Miss

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Writing Policies

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Cache Mapping

Index0

1

2

3

4

5

...

Index0

1

2

3

Index0

1

2

3

4

5

...

Index0

1

2

3

Direct Mapped 2-Way Associative

Memory Cache Memory Cache

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Cache Miss

0,0 0,1 0,2 0,3

1,0 1,1 1,2 1,3

2,0 2,1 2,2 2,3

3,0 3,1 3,2 3,3

Row Major

Col

umn

Maj

or#define MAX 4double A[MAX][MAX], x[MAX], y[MAX];

/* Initialize A and x, assign y=0 */

for (i=0; i<MAX, i++) for (j=0; j<MAX; j++) y[i]+=A[i][j]*x[j];

/* Assign y=0 */

for (j=0; j<MAX, j++) for (i=0; i<MAX; i++) y[i]+=A[i][j]*x[j];

Cache Memory

How many hit misses?

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Cache CoherenceCore 0

Cache 0

Core 1

Cache 1

Interconnect

x=2 y1

y0 z1

Time Core 0 Core 10 y0=x; y1=3*x;

1 x=7; Statements without x

2 Statements without x z1=4*x;

What is the value of z1?

With write through policy …

With write back policy …

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Cache Coherence

Core 0

A

Core 1

A

A=5

A=5 B=A2

update A reload Ainvalidate

(A=5)B

Core 0

AB

Core 1

AB

A=5 B=B+1

update AB reload ABinvalidate

A and B are called false sharing.

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False Sharing

int i, j, m, n;double y[m];

/* Assign y=0 */

for (i=0; i<m; i++) for (j=0; j<n; j++) y[i]+=f(i, j);

/* Private variables */int i, j, iter_count;

/* Shared variables */int m, n, core_count;double y[m];

iter_count=m/core_count;

/* Core 0 does this */for (i=0; i<iter_count; i++) for (j=0; j<n; j++) y[i]+=f(i, j);

/* Core 1 does this */for (i=iter_count; i<2*iter_count; i++) for (j=0; j<n; j++) y[i]+=f(i, j);

m=8, two cores

cache line: 64 bytes

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Virtual Memory• Virtualization of various forms of computer data storage

into a unified address space– Logically increases the capacity of main memory (e.g.,

DOS can only access 1 MB of RAM).

• Page– A block of continuous virtual memory addresses– The smallest unit to be swapped in/out of main memory

from/into secondary storage.

• Page Table– Used to store the mapping between virtual addresses

and physical addresses.

• Page Fault– The accessed page is not in the physical memory.

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Interleaving Statements

s1

s2

s1

s2

T0 T1

s1 s1 s1 s1 s1s1

s2

s1

s2

s1

s2

s2

s1

s2

s2

s1

s2

s2

s1

s2

s2

s2

s1

s2

!!)!(

NMNMCM

NM

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Critical Region

• A portion of code where shared resources are accessed and updated

• Resources: data structure (variables), device (printer)

• Threads are disallowed from entering the critical region when another thread is occupying the critical region.

• A means of mutual exclusion is required.

• If a thread is not executing within the critical region, that thread must not prevent another thread seeking entry from entering the region.

• We consider two threads and one core in the following examples.

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First Attempt

int threadNumber = 0;

void ThreadZero(){ while (TRUE) do { while (threadNumber == 1) do {} // spin-wait CriticalRegionZero; threadNumber=1; OtherStuffZero; }}

void ThreadOne(){ while (TRUE) do { while (threadNumber == 0) do {} // spin-wait CriticalRegionOne; threadNumber=0; OtherStuffOne; }}

• Q1: Can T1 enter the critical region more times than T0?

• Q2: What would happen if T0 terminates (by design or by accident)?

79

Second Attempt

int Thread0inside = 0;int Thread1inside = 0;

void ThreadZero(){ while (TRUE) do { while (Thread1inside) do {} Thread0inside = 1; CriticalRegionZero; Thread0inside = 0; OtherStuffZero; }}

void ThreadOne(){ while (TRUE) do { while (Thread0inside) do {} Thread1inside = 1; CriticalRegionOne; Thread1inside = 0; OtherStuffOne; }}

• Q1: Can T1 enter the critical region multiple times when T0 is not within the critical region?

• Q2: Can T1 and T2 be allowed to enter the critical region at the same time?

80

Third Attempt

int Thread0WantsToEnter = 0;int Thread1WantsToEnter = 0;

void ThreadZero(){ while (TRUE) do { Thread0WantsToEnter = 1; while (Thread1WantsToEnter) do {} CriticalRegionZero; Thread0WantsToEnter = 0; OtherStuffZero; }}

void ThreadOne(){ while (TRUE) do { Thread1WantsToEnter = 1; while (Thread0WantsToEnter) do {} CriticalRegionOne; Thread1WantsToEnter = 0; OtherStuffOne; }}

81

Fourth Attempt

int Thread0WantsToEnter = 0;int Thread1WantsToEnter = 0;

void ThreadZero(){ while (TRUE) do { Thread0WantsToEnter = 1; while (Thread1WantsToEnter) do { Thread0WantsToEnter = 0; delay(someRandomCycles); Thread0WantsToEnter = 1; } CriticalRegionZero; Thread0WantsToEnter = 0; OtherStuffZero; }}

void ThreadOne(){ while (TRUE) do { Thread1WantsToEnter = 1; while (Thread0WantsToEnter) do { Thread1WantsToEnter = 0; delay(someRandomCycles); Thread1WantsToEnter = 1; } CriticalRegionOne; Thread1WantsToEnter = 0; OtherStuffOne; }}

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Dekker’s Algorithmint Thread0WantsToEnter = 0, Thread1WantsToEnter = 0, favored = 0;void ThreadZero(){ while (TRUE) do { Thread0WantsToEnter = 1; while (Thread1WantsToEnter) do { if (favored == 1) { Thread0WantsToEnter = 0; while (favored == 1) do {} Thread0WantsToEnter = 1; } } CriticalRegionZero; favored = 1; Thread0WantsToEnter = 0; OtherStuffZero; }}

void ThreadOne(){ while (TRUE) do { Thread1WantsToEnter = 1; while (Thread0WantsToEnter) do { if (favored == 0) { Thread1WantsToEnter = 0; while (favored == 0) do {} Thread1WantsToEnter = 1; } } CriticalRegionOne; favored = 0; Thread1WantsToEnter = 0; OtherStuffZero; }}

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Parallel Program Design• Foster’s Methodology

• Partitioning– Divide the computation to be performed and the data operated on by the computation into

small tasks.

• Communication– Determine what communication needs to be carried out among the tasks.

• Agglomeration– Combine tasks that communicate intensively with each other or must be executed sequentially

into larger tasks.

• Mapping– Assign the composite tasks to processes/threads to minimize inter-processor communication

and maximize processor utilization.

84

Parallel Histogram

10 2 3 4 5

data[i-1]

bin_counts[b-1]++ bin_counts[b]++

Find_bin()

Increment bin_counts

data[i] data[i+1]

85

Parallel Histogram

data[i-1]

loc_bin_cts[b-1]++

data[i] data[i+1]

data[i+2]

loc_bin_cts[b]++

bin_counts[b-1]+= bin_counts[b]+=

loc_bin_cts[b-1]++ loc_bin_cts[b]++

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Performance

• Speedup

• Efficiency

• Scalability– Problem Size, Number of Processors

• Strongly Scalable– Same efficiency for larger N with fixed problem size

• Weakly Scalable– Same efficiency for larger N with a fixed problem size per processor

Parallel

Serial

TTS

Parallel

Serial

TNT

NSE

87

Amdahl's Law

NPP

NS

)1(

1)(

88

Gustafson's Law

baTParallel bNaTSerial

sequential parallel

baaforNN

babNaNS

)1()(

• Linear speedup can be achieved when:– Problem size is allowed to grow monotonously with N.– The sequential part is fixed or grows slowly.

• Is it possible to achieve super linear speedup?

89

Review

• Why is parallel computing important?

• What is data dependency?

• What are the benefits and issues of fine-grained parallelism?

• What are the three types of parallelism?

• What is the difference between concurrent and parallel computing?

• What are the essential features of cloud computing?

• What is Flynn’s Taxonomy?

90

Review

• Name the four categories of memory systems.

• What are the two common cache writing policies?

• Name the two types of cache mapping strategies.

• What is a cache miss and how to avoid it?

• What may cause the false sharing issue?

• What is a critical region?

• How to verify the correctness of a concurrent program?

91

Review

• Name three major APIs for parallel computing.

• What are the benefits of GPU computing compared to MapReduce?

• What is the basic procedure of parallel program design?

• What are the key performance factors in parallel programming?

• What is a strongly/weakly scalable parallel program?

• What is the implication of Amdahl's Law?

• What does Gustafson's Law tell us?