1. How fast are Supercomputers ? Covering: FLOPS, How fast?, TOP500
Dr. Show’ichi Furuyama
National Institute of Technology, Toyama College, Japan
Good morning everyone. Thank you all for coming to my lecture again.
Today we will about the abilities of super computers. “How fast are Supercomputers?” is today’s title.
Please keep your questions and comment until the end of my lecture.
We will be covering three main points today. First is FLOPS, Second is “how fast?” and third is TOP 500. Have you ever heard “supercomputer” ?
And do you know What/Where/How fast is the fastest supercomputer in the world?
By the end of my talk, you’ll understand these topics.
OK, let’s get started.

2. How many “+” and “-” can you find?
Please answer the following calculation !
and
please measure your calculation time! = = =
At first, I would like you to answer this easy calculation. I prepared three questions. Please measure your calculation time by your watch. Ready, set, go !
(30 seconds waiting…)
Anyone finished? Ok next. Please count “+” and “-” operations in the calculation? The no.1 has three operations. How many operations do you find in three equations ? 10 ! that’s right!
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Well done / nice work / excellent /
How many “+” and “-” can you find?

3. How many operations could you calculate
in one second ?
𝟏𝟎 [𝒐𝒑𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝒔] 𝑪𝒂𝒍𝒄. 𝒕𝒊𝒎𝒆 [𝒔𝒆𝒄] = ??
FLoating-point Operations Per Second (FLOPS)
= 𝑵. 𝒐𝒇 𝑶𝒑𝒆𝒓𝒂𝒕𝒊𝒐𝒏𝒔 𝑪𝒂𝒍𝒄. 𝒕𝒊𝒎𝒆 [𝒔𝒆𝒄]
+, −, ×, ÷
Your next task is “How many operations could you calculate in one second?” You can calculate it by the equations. What is your result?
The numeric value is called FLOPS. Flops means Floating-point operations per second. Floating-point operation means operation for decimal fraction. In the case they are plus, minus, multiply and division. In short, it is how many operations computer can calculate. The value is indicator of processing ability of computers.
Anyway, how much processing ability of computer is required for a simulation?

4. Inside of Ocean Simulation
Making computational cells
Calculate equations in all cells
𝑎 11 𝒙 𝟏 + 𝑎 12 𝒙 𝟐 ⋯+ 𝑎 1𝑖 𝒙 𝒊 +⋯+ 𝑎 1𝑛 𝒙 𝒏 = 𝒃 𝟏 ⋮
𝑎 𝑖 1 𝒙 𝟏 + 𝑎 𝑖 2 𝒙 𝟐 ⋯+ 𝑎 𝑖 𝑖 𝒙 𝒊 +⋯+ 𝑎 𝑖 𝑛 𝒙 𝒏 = 𝒃 𝒊
𝑎 𝑛1 𝒙 𝟏 + 𝑎 𝑛2 𝒙 𝟐 ⋯+ 𝑎 𝑛𝑖 𝒙 𝒊 +⋯+ 𝑎 𝑛𝑛 𝒙 𝒏 = 𝒃 𝒏
𝑎 11 𝑎 12 ⋯⋯⋯⋯ 𝑎 1𝑛 𝑎 21 𝑎 22 ⋯⋯⋯⋯ 𝑎 2𝑛 ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ ⋮ ⋱ ⋮ 𝑎 𝑛1 𝑎 𝑛2 ⋯⋯⋯⋯ 𝑎 𝑛𝑛 𝒙 𝟏 𝒙 𝟐 𝒙 𝟑 ⋮ 𝒙 𝒊 ⋮ 𝒙 𝒏−𝟏 𝒙 𝒏 = 𝒃 𝟏 𝒃 𝟐 𝒃 𝟑 ⋮ 𝒃 𝒊 ⋮ 𝒃 𝒏−𝟏 𝒃 𝒏
In the last class, I told you what supercomputers calculate? I showed this slide. These are computational cells for an ocean simulation. We made simultaneous equations on each computational cells. Finally I introduced that the supercomputer calculates a huge matrix. However the equations are general form. So the next, let’s see the actual equations for the ocean simulation.

5. Equations for Ocean Simulation
𝜼 𝒊,𝒋 𝒌+𝟏 = 𝜼 𝒊,𝒋 𝒌 − 𝜟𝒕 𝜟𝒙 × 𝑴 𝒊+𝟏/𝟐,𝒋 𝒌+𝟏/𝟐 − 𝑴 𝒊−𝟏/𝟐,𝒋 𝒌+𝟏/𝟐 − 𝜟𝒕 𝜟𝒚 × 𝑵 𝒊,𝒋+𝟏/𝟐 𝒌+𝟏/𝟐 − 𝑵 𝒊,𝒋−𝟏/𝟐 𝒌+𝟏/𝟐
8 operations
𝑴 𝒊+𝟏/𝟐,𝒋 𝒌+𝟏/𝟐 = 𝑴 𝒊+𝟏/𝟐,𝒋 𝒌−𝟏/𝟐 −𝒈 ×𝑫 𝒊+𝟏/𝟐,𝒋 𝒌 × 𝜟𝒕 𝜟𝒙 × 𝜼 𝒊+𝟏,𝒋 𝒌 − 𝜼 𝒊,𝒋 𝒌
6 operations
𝑵 𝒊,𝒋+𝟏/𝟐 𝒌+𝟏/𝟐 = 𝑵 𝒊,𝒋+𝟏/𝟐 𝒌−𝟏/𝟐 −𝒈 ×𝑫 𝒊,𝒋+𝟏/𝟐 𝒌 × 𝜟𝒕 𝜟𝒚 × 𝜼 𝒊,𝒋+𝟏 𝒌 − 𝜼 𝒊,𝒋 𝒌
Please look at these equations. The ocean simulation uses them. You don’t have to understand the meanings of equations at the moment. But please count the number of operations in these equations.
The eta means water elevation. How many operations can you see in it? Yes, you can see eight operations in it.
And following equations are for the M and N. Those mean fluxes. The quantity are product of velocity and volume. They had 6 operations each other.
As a result it is 20 operations in each computational cell. If your FLOPS is nearly 1, you need to calculate these equations for nearly 20 seconds. In the ocean simulation case, we used over 12K cells, so about 300K operations are required for one time step simulation.
If your FLOPS is ‘1’, you need 3.5 days for the calculation. We strongly want to use fast computer for the simulation !
By the way, how fast is computers?… lets see a history of the supercomputers.
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That’s correct / yes, that’s right / close not quite
6 operations
Total operations/cell
Total Num. of Cells: 15,000 　→ ,000 operations/timestep
If your FLOPS is ‘1’, you need 300,000 [sec]　→
3.5 [days]

6. History of Super Computer
Name
FLOPS
Year
ENIAC
300
1946
The 1st computer (USA)
Cray-1
250,000,000
1976
Cray (USA)
FACOM VP-100
1982
Fujitsu (JPN)
CM-5
65,500,000,000
1993
TM (USA)
NWT
170,400,000,000
1994
NAL & Fujitsu (JPN)
T3E
1,020,000,000,000
1998
Earth Simulator
35,860,000,000,000
2002
JAMSTEC & NEC (JPN)
Blue Gene
280,600,000,000,000
2005
LANL & IBM (USA)
MFLOPS
GFLOPS
TFLOPS
OK next, let’s focus on the history of super computer.
ENIAC is the first supercomputer in the history. It was made in 1946 and it had 300 flops ability. It was nearly 300 times faster than we came out.
In the mid 70s to mid 80s the calculation ability exceeded mega flops.
And in the early 90s, the ability achieved giga flops level. You can see the CM-5 in left photo. Personally the CM-5 is a memorable machine for me because I used the machine for my master’s thesis.
In the late 90s to early 2000, the T3E reached tera flops. I used the machine for my doctoral thesis. So I have a lot of memories of the machine. It is a photo of T3E.
By the way, I asked you which CPU is in your laptop. A lot of answers were intel Core i7. How fast is your laptop? It is from 50 – 224 GFLOPS. The ability is similar to CM-5, it was a fastest supercomputer in the world in It was very big like as a photo and 1,024 CPUs were connected, but now you can use the same ability computer personally and you can use when you want to use it. It is impressive situation for me because I used CM-5.
© LANL
©Cray
Thinking Machine CM-5
Cray T3E
How fast is Core i7 ?
Your laptop : 50 – 224 GFLOPS

7. 1st – 5th Ranking of Top 500 List (November 2013)
Country
System
Rmax
(TFLOPS) 1
China
Tianhe-2
(MilkyWay-2) 2
USA
Titan 3
Sequoia 4
Japan K 5
Mira
8586.6
Top500 List – November 2013
K : 103
M : 106
G : 109
T : 1012
P : 1015
Finally I will introduce the latest supercomputing ability. Every June and November, the top 500 fastest supercomputers are listed June’s result will be opened on the 23rd of this month. So I’ll show the November 2013 list. The fastest computer is MilkyWay-2 in China. This ability is 33 peta Flops. Peta is 10 to the power of 15, and the K in Japan is the 4th fastest computer. It is 10 peta flops.
In the 3rd section of lecture, I would like to talk about the K computer.

8. K Computer Origin of Name : 一京 = 1016 = 10 Peta (C) RIKEN
𝐾 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑌𝑜𝑢𝑟 𝑙𝑎𝑝𝑡𝑜𝑝 = 10,000,000 [𝐺𝐹𝐿𝑂𝑃𝑆] 224 [𝐺𝐹𝐿𝑂𝑃𝑆] =
By the way, do you know the origin of name of K computer?
In Japan, the unit of 10 to the power of 16 is called KEI. The engineers named the computer in the hope to achieve 10 peta flops. When I heard the story, I felt strong passion of Japanese enginner.
Let’s check the K’s ability. Your laptop has 224 giga flops. The K is 10 peta flops, so about 44 thousand times faster than your laptop. Can you imagine the calculation speed?
And next. The comparing with your ability. In one second, K can calculate 10 peta operations. On the other hand, you can calculate 1 operation. When will we finish the task for 1 second of K computer.
It will be 317 m years after…. It is incredible power of K.
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June 2011 & Nov fastest machine in TOP500
Fujitsu :
864 Racks in 50m x 60m room (basketball coat 28x15 m, 6-7 times bigger)
44,642 (times faster)
𝐾 𝑐𝑜𝑚𝑝𝑢𝑡𝑒𝑟 𝑌𝑜𝑢 = 10 [𝑃𝐹𝐿𝑂𝑃𝑆] 1 [𝐹𝐿𝑂𝑃𝑆]
→　317,098,082 [years]

9. Summary FLOPS (FLoating-Point Operations Per Second)
How many ‘+ - x / ‘ in 1 second ?
Indicator of ability.
How fast is that ?
You : ～ 1 FLOPS ?
History of Supercomputers
Laptop : 200 GFLOPS
TOP500 in November 2013
Top : Milky-way 2 (China) 33 PFLOPS
4 th : K computer (Japan) 10 PFLOPS
44,000 times faster than laptop
317 million years human’s task for K’s 1 second task
OK, I’ve now come to the end of my talk. I would like to summarize the lecture.
The first I talked to you today about FLOPS. It was a indicator of ability for computer. And we calculated about ourselves ability. It was 0.5 – 1.0 flops. Next I talked about history of supercomputers and we get information of our laptop’s ability. Our laptop’s ability is estimated about 200 gflops.
And finally I introduced latest result of fastest computer in the world. It is Milky-way 2 in China. It has 33 pflops ability.
And K is 4th fastest computer and the ability is 10 pflops. It is 44,000 times faster than laptop. And when you explain the supercomputer to anybody, please remember what I said “Supercomputer’s 1 second task is similar with 317 million years task for person….”
Thank you all for listening , it was a pleasure being here today. Thanks again.