慶應義塾大学
2015年度 秋学期

コンピューター・アーキテクチャ
Computer Architecture

2015年度秋学期　月曜日3限 (Fall 2015, Mondays 3rd period)
　 科目コード: 35010 / 2単位
カテゴリ:
開講場所：SFC
授業形態：講義
担当: Rodney Van Meter
E-mail: rdv@sfc.keio.ac.jp

第2回 10月05日 Lecture 2, October 05:
Faster!

Outline of This Lecture

Rescheduling October 19 Lecture

I will be out of town on October 19, so lecture for that day will be rescheduled. Since it is a fairly standalone lecture, the order of lectures won't be changed, we will do that one at some other date, TBD. Please do come when it is scheduled, since that lecture is one of the most fun of the semester!

Performance Measurement

Last week, we discussed some performance graphs, plotting (a) wall-clock time, (b) speedup, and (c) efficiency versus the number of threads used on a particular problem. This week, each of you will see how to take that data, and how to recreate the graphs. You need R, an account on a Unix-like machine with more than one core and an OpenMP-capable compiler, and the code available from the link below at Homework.

Note on compilers: On the Mac, Apple's supplied compiler is called gcc, but it is really the Clang compiler, not the true GNU gcc. That would be fine, since it's mostly compatible, but there are some features of one not present in the other. In particular, for this exercise you will need the parallel extensions for C known as OpenMP, and Clang does not provide them. You can install gcc5 (or gcc4) for Mac on your machine, or you can install a Vagrant VirtualBox. I have done both. If you want to use gcc-5 on your Mac, remember to change the first line in both Makefiles to: 

CC=gcc-5

That should allow you to compile the OpenMP program properly.

  1. Get the tarball.
  2. Unpack it using tar xvfz.
  3. Confirm that two of the parameters are reasonable. Look at the top of main.c, where you should see 
    #define LOOP 1000
#define REGISTER_SIZE 20
    Edit the file and fix those parameters, if they are different.
  4. Build both the library and the program hw1 using make.
  5. Execute time ./hw1 and record the results in a file that looks like 
    1 440 435 0.2
2 229 451 0.36
3 161 475 0.42
4 122 482 0.4
  6. You will want to run this with various parameters, including the number of threads, possibly the number of loops, and the register size.
  7. Back on your laptop, in R, using the file fun.R or by hand, you can plot the results using commands like 
    > ARMDATA1 <- matrix(scan("armstrong-one-run.dat"),ncol=4,byrow=T)
Read 48 items
> plot(ARMDATA1[,1],ARMDATA1[,2])
> x <- seq(1,16)
> y = 440/x
> points(x,y,type="l")
> help(plot)
> plot(ARMDATA1[,1],ARMDATA1[,2],log="y")
> points(x,y,type="l")
> plot(ARMDATA1[,1],ARMDATA1[,2],log="xy")
> points(x,y,type="l")

Here is some data I took this morning:

Van-Meter-Rodneys-MacBook-Pro:vagrant-files rdv$ vagrant up
Bringing machine 'default' up with 'virtualbox' provider...
==> default: Clearing any previously set forwarded ports...
==> default: Clearing any previously set network interfaces...
==> default: Preparing network interfaces based on configuration...
    default: Adapter 1: nat
==> default: Forwarding ports...
    default: 22 => 2222 (adapter 1)
==> default: Running 'pre-boot' VM customizations...
==> default: Booting VM...
==> default: Waiting for machine to boot. This may take a few minutes...
    default: SSH address: 127.0.0.1:2222
    default: SSH username: vagrant
    default: SSH auth method: private key
    default: Warning: Connection timeout. Retrying...
    default: Warning: Remote connection disconnect. Retrying...
==> default: Machine booted and ready!
==> default: Checking for guest additions in VM...
==> default: Mounting shared folders...
    default: /vagrant => /Users/rdv/new/quantum/vagrant-files
==> default: Machine already provisioned. Run `vagrant provision` or use the `--provision`
==> default: to force provisioning. Provisioners marked to run always will still run.
Van-Meter-Rodneys-MacBook-Pro:vagrant-files rdv$ vagrant ssh
Last login: Mon Oct  5 00:17:27 2015 from 10.0.2.2
-bash: warning: setlocale: LC_CTYPE: cannot change locale (UTF-8): No such file or directory
[vagrant@localhost ~]$ more /proc/cpuinfo
processor	: 0
vendor_id	: GenuineIntel
cpu family	: 6
model		: 70
model name	: Intel(R) Core(TM) i7-4750HQ CPU @ 2.00GHz
stepping	: 1
cpu MHz		: 1997.136
cache size	: 6144 KB
physical id	: 0
siblings	: 4
core id		: 0
cpu cores	: 4
apicid		: 0
initial apicid	: 0
fpu		: yes
fpu_exception	: yes
cpuid level	: 5
wp		: yes
flags		: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pa
t pse36 clflush mmx fxsr sse sse2 ht syscall nx rdtscp lm constant_tsc rep_good pn
i ssse3 lahf_lm
bogomips	: 3994.27
clflush size	: 64
cache_alignment	: 64
address sizes	: 39 bits physical, 48 bits virtual
power management:

processor	: 1
vendor_id	: GenuineIntel
cpu family	: 6
model		: 70
model name	: Intel(R) Core(TM) i7-4750HQ CPU @ 2.00GHz
stepping	: 1
cpu MHz		: 1997.136
cache size	: 6144 KB
physical id	: 0
siblings	: 4
core id		: 1
cpu cores	: 4
apicid		: 1
initial apicid	: 1
fpu		: yes
fpu_exception	: yes
cpuid level	: 5
wp		: yes
flags		: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pa
t pse36 clflush mmx fxsr sse sse2 ht syscall nx rdtscp lm constant_tsc rep_good pn
i ssse3 lahf_lm
bogomips	: 3994.27
clflush size	: 64
cache_alignment	: 64
address sizes	: 39 bits physical, 48 bits virtual
power management:

processor	: 2
vendor_id	: GenuineIntel
cpu family	: 6
model		: 70
model name	: Intel(R) Core(TM) i7-4750HQ CPU @ 2.00GHz
stepping	: 1
cpu MHz		: 1997.136
cache size	: 6144 KB
physical id	: 0
siblings	: 4
core id		: 2
cpu cores	: 4
apicid		: 2
initial apicid	: 2
fpu		: yes
fpu_exception	: yes
cpuid level	: 5
wp		: yes
flags		: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pa
t pse36 clflush mmx fxsr sse sse2 ht syscall nx rdtscp lm constant_tsc rep_good pn
i ssse3 lahf_lm
bogomips	: 3994.27
clflush size	: 64
cache_alignment	: 64
address sizes	: 39 bits physical, 48 bits virtual
power management:

processor	: 3
vendor_id	: GenuineIntel
cpu family	: 6
model		: 70
model name	: Intel(R) Core(TM) i7-4750HQ CPU @ 2.00GHz
stepping	: 1
cpu MHz		: 1997.136
cache size	: 6144 KB
physical id	: 0
siblings	: 4
core id		: 3
cpu cores	: 4
apicid		: 3
initial apicid	: 3
fpu		: yes
fpu_exception	: yes
cpuid level	: 5
wp		: yes
flags		: fpu vme de pse tsc msr pae mce cx8 apic sep mtrr pge mca cmov pa
t pse36 clflush mmx fxsr sse sse2 ht syscall nx rdtscp lm constant_tsc rep_good pn
i ssse3 lahf_lm
bogomips	: 3994.27
clflush size	: 64
cache_alignment	: 64
address sizes	: 39 bits physical, 48 bits virtual
power management:

[vagrant@localhost ~]$ 
[vagrant@localhost ~]$ cd architecture/
[vagrant@localhost architecture]$ ls
architecture-hw1-111007.tgz  data  src
[vagrant@localhost architecture]$ cd src
[vagrant@localhost src]$ ls
AAAREADME.txt  hw1  qulib
[vagrant@localhost src]$ cd hw1/
[vagrant@localhost hw1]$ ls
Makefile  hw1  main.c  main.o
[vagrant@localhost hw1]$ time ./hw1

real	0m7.044s
user	0m27.129s
sys	0m1.013s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=1
[vagrant@localhost hw1]$ time ./hw1

real	0m10.428s
user	0m10.386s
sys	0m0.038s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=2
[vagrant@localhost hw1]$ time ./hw1

real	0m7.412s
user	0m14.370s
sys	0m0.447s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=3
[vagrant@localhost hw1]$ time ./hw1

real	0m6.995s
user	0m20.348s
sys	0m0.625s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=4
[vagrant@localhost hw1]$ time ./hw1

real	0m6.860s
user	0m26.468s
sys	0m0.943s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=5
[vagrant@localhost hw1]$ time ./hw1

real	0m7.361s
user	0m21.475s
sys	0m1.526s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=6
[vagrant@localhost hw1]$ time ./hw1

real	0m7.391s
user	0m21.657s
sys	0m1.494s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=8
[vagrant@localhost hw1]$ time ./hw1

real	0m6.954s
user	0m20.681s
sys	0m1.600s
[vagrant@localhost hw1]$ export OMP_NUM_THREADS=16
[vagrant@localhost hw1]$ time ./hw1

real	0m6.762s
user	0m20.034s
sys	0m2.429s
[vagrant@localhost hw1]$

I ran this on a Vagrant VirtualBox running CentOS on my Mac. You can see that the performance improvement was only modest. Why do you think that is?

定量てきなデザイン概念
Quantitative Principles of Design

Let's talk about Hennessy & Patterson's Five Principles:

  1. Take Advantage of Parallelism
  2. Principle of Locality
  3. Focus on the Common Case
  4. Amdahl's Law
  5. The Processor Performance Equation
I would add to this one imperative: Achieve Balance.

Take Advantage of Parallelism

Parallelism can be found by using multiple processors on different parts of the problem, or multiple functional units (floating point units, disk drives, etc.), or by pipelining, dividing an individual computer instruction into several parts and executing the parts of different instructions at the same time in different parts of the CPU.

Principle of Locality

Programs and data tend to reuse data and instructions that have been recently used. There are two forms of locality: spatial and temporal. Locality is what allows a cache memory to work.

Focus on the Common Case

The things that are done a lot should be fast; the things that are rare may be slow.

Amdahl's Law

Amdahl's Law tells us how much improvement is possible by making the common case fast, or by parallelizing part of the algorithm. In the example below, 3/5 of the algorithm can be parallelized, meaning that three times as much hardware applied to the problem gains us only a reduction from five time units to three.

Example of Amdahl's Law, parallel and serial portions.

Some problems, most famously graphics, are known as "embarrassingly parallel" problems, in which extracting parallelism is trivial, and performance is primarily determined by input/output bandwidth and the number of processing elements available. More generally, the parallelism achievable is determined by the dependency graph. Creating that graph and scheduling operations to maximize the parallelism and enforce correctness is generally the shared responsibility of the hardware architecture and the compiler.

Dependency graph for the above figure.

プロセッサー・パフォマンス定式
The Processor Performance Equation

CPU time = (seconds )/ program = (Instructions )/ program × (Clock cycles )/ Instruction × (Seconds )/ Clock cycle

What's in a Computer?

(Here's the fun part...)

Wikipedia motherboard block diagram

宿題
Homework

The source you need, including script files, are available in a tar file here.

The specification for OpenMP, and a "summary card" for C and C++, are available here. The latest version is 3.1, but there is a Japanese version of the 3.0 spec available. 最新のバージョンは3.1だが、3.0の日本語版はあり ますよ！

This week's homework (submit via SFS, due 10/19):

  1. Replot the data from our simple parallel program. How much faster does it get? Is the speedup the same for all problem sizes?
  2. In architecture/src/qulib/sim.c, you will find the functions cnot() and Hadamard(). In the statement
    /* XXX parallelizing this loop is tricky, but it's a "big" loop, so worth doing... */
#pragma omp parallel for schedule(static,8192) private(j,k,z)

    the number 8192 indicates the size of the chunk of the large array that each thread executes. Change that number both smaller and larger in both functions to see the effects. Save these as separate data sets, and plot them all together on one plot.
    1. First, eliminate the "schedule" altogether; try it with
      #pragma omp parallel for private(j,k,z)
    2. Next, try it with schedule(static,16).
    3. schedule(static,256).
    4. schedule(static,1024).
    5. schedule(static,4096).
    6. schedule(static,16384).
    7. By now, you should have some idea of what values will work well. Choose the optimal value for the schedule size for this application and machine.
  3. Plot the results with different numbers of threads in a set of graphs like the ones from last week. You can put all of the data on one graph (giving you three graphs, total) or on separate graphs.

Next Lecture

Next lecture:

第3回 10月12日 プロセッサー：命令の基本
Lecture 3, October 12: Processors: Basics of Instruction Sets

以下で、P-Hはコンピュータの構成と設計~ハードウエアとソフトウエアの インタフェース 第3版、 H-Pはコンピュータアーキテクチャ 定量的アプローチ 第4版.

Below, P-H is Computer Organization and Design: The Hardware-Software Interface, and H-P is Computer Architecture: A Quantitative Approach.

Readings for next time:

Additional Information

その他