1. Krzysztof Rojek, CTO, byteLAKE
krojek@byteLAKE.com
6TH INTERNATIONAL EULAG USERS WORKSHOP
MAY 29, 2018, 14:00-14:45

2.  Area: Adaptation of a real-life scientific codes to the most advanced
computing architectures.
 Challenge: Device architectures are constantly changing. Current
architectures are very various. Our codes need to be very portable
and flexible.
 Goal: Take HPC to the "Industry 4.0" by implementing smart techniques
to optimize the codes in terms of performance and energy
consumption.
2

3.  Piz Daint (ranked 3-rd at top 500):
 GPU: NVIDIA Tesla P100 - PASCAL
 1xGPU per node
 Single GPU design
 5320 nodes (up to 36 used in this work)
 Calculation speed: float is 2x faster
than double
 MICLAB:
 GPU: NVIDIA Tesla K80 - KEPLER
 2xGPUs per node
 Dual GPU design
 2 nodes (remaining nodes with Intel
Xeon Phi)
 Calculation speed: float is 3x faster
than double
3
 Size of data transfer between nodes: 2x less using float than double
 No access to sudo user – it makes a problem when your code is based on DVFS
Expectation: Mixed precision arithmetic allows us to reduce the energy consumption
and execution time; It can be used in the real HPC platforms (without special access)

4.  Stencil-based algorithm for numerical simulation of
geophysical fluids flows on micro-to-planetary scales:
 7 stencils (compressed into 4 kernels) – each
depends on one or more others (343 flops-per-el.)
 Iterative algorithm – a single iteration represents one
time step
 11 matrices:
 x, xP – scalar quantity (i.e. temperature); input/output
matrices between time steps
 v1, v2, v3, v1P, v2P, v3P – velocity vectors in i, j, and k
directions
 h – density matrix
 cp, cn – temporary, intermediate matrices
4
xP
x
xPKernel 3
Kernel 2
Kernel 1
Kernel 0 xP
v1P v2P
cp
xP
cn
v3P
Outputs:
(x,v1,v2,v3,h)
(v1,v2,v3,h,xP)
(x,h,xP,v1P,v2P,v3P)
(x,h,v1P,v2P,v3P,cp,cn)
Inputs:

5.  Idea: Provide a highly parametrized code in order to easily map the algorithm onto GPU
 Mapping: Select the right values of given code parameters (configuration) in terms of
desired criterion (Energy consumption)
 How to: We build the search space of possible configurations and prune it using our
machine learning module (MLM)
 MLM: It is still the ongoing task. Here we propose to apply the modified random forest
algorithm.
5

6.  We can use different number of:
 Streams count (SPG)
 Nodes count (NDS)
 With different topologies:
 Topology of streams (TGP)
 Topology of nodes (TDS)
6
1x1 1x2
1x1
2x1
1x1
1x1
2x1
1x2
2x2
1x1 1x2 1x3 1x4
1x1
2x1
3x1
4x1
Stream/Node: 1
Topology: 1
Streams/Nodes: 2
Topologies: 2
Streams/Nodes: 4
Topologies: 3

7. 7
Synchronize domain
Synchronize domain
Synchronize domain
Synchronize domain
Synchronize domain
Synchronize domain
Synchronize domain
Synchronize domain
Kernel 0
Kernel 1
Kernel 2
Kernel 3
Data transfer
Kernel 0
Kernel 1
Kernel 2
Kernel 3
Data transfer
vs.
 Each stream
works on
distributed
subdomains
 Computations
are
independent
within a single
time step
 Halo exchange
is required after
each time step
 Each stream
share the same
subdomain
 Computations
depends on the
neighboring
streams
 Halo exchange
is not required
within a single
node

8.  By selecting the right strategy of
halo exchanging we can focus
on more parallelism or less
operations
 We can use a different strategy
within node and between nodes
8
Halo
exchange
cudaMemcpy
Buffers
GPU direct No GPU direct
No-buffers
Kernels
Single kernel Two kernels

9.  We takes into consideration also some basic parameters:
 CUDA block sizes for each of 4 kernels
 CUDA blocks are of size X times Y, where
 X*Y mod 32 = 0
 X>=Y
 X mod 16 =0
 X*Y <= 1024
 X<=M and Y<=N, where NxMxL is a size of the grid
 Data alignment and padding within a range from 1 to 4096 B
 Align in: {1, 2, 4, 8, …, 4096}
9

10.  Assumption: We believe that we can find a really good configuration by testing about 5000
configurations from the search space (more that this is too expensive)
 We consider two possible approaches:
 Positive: Find good solutions and eliminate groups that seem to be worse than ours
 Risk: When we find a branch with a good solution we can eliminate other branches (also quite good) that should
be worse. In fact we can eliminate a branch containing the best solution.
 Negative: Find bad solutions and eliminate them
 Risk: When we find branches with bad solutions we can eliminate them although the worst one can be still in (the
best one also is there).
 Fact: We test random branches (we may not select the best or the worst one); we are searching
for the suboptimal solution.
10

11.  Precision:
 DOUBLE
 Diameter:
 28.0
 L2 norm:
 0.0746
 Diffusion error:
 1.7503
 Phase error:
 0.7576
11
Halo exchange
(xP or x)

12.  Precision: DOUBLE
 Diameter: 28.0
 L2 norm: 0.0746
 Diff. err.: 1.7503
 Phase err.: 0.7576
 Precision: FLOAT
 Diameter: 28.0
 L2 norm: 0.1301
 Diff. err.: 2.2439
 Phase err.: 7.5919
12
FloatDouble

13.  Goal: Reduce the energy consumption
 Condition: Keep the accuracy at a high level (1% loss is
acceptable)
 Assumptions:
 The proposed method is intended to iterative algorithms
 Dynamic approach, self adaptable to a particular
simulation
 Self adaptation is done based on the short training stage
(the first 11 time steps)
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1. Change
the i-th
matrix from
DP to SP
2. Execute a
single time
step
3. Measure
Energy and
Accuracy
4. Restore
the i-th
matrix to DP
Training stage:
Traditional approach based on static selection of precision arithmetic
is less flexible and may be too restrictive for some simulations

14. 14
0
10
20
30
40
50
60
70
80
90
100
0/4 1/4 2/4 3/4 4/4
ENERGYCONSUMPTION[%]
PART OF A SINGLE SOLID BODY ROTATION
Change the
precision of
the i-th matrix
from DP to SP
0
10
20
30
40
50
60
70
80
90
100
0/4 1/4 2/4 3/4 4/4
ACCURACYLOSS[%]
PART OF A SINGLE SOLID BODY ROTATION
DOUBLE
Change the
precision of
the i-th matrix
from DP to SP
Should be
minimizedShould be
maximized
ΔE
ΔA

15. 15
 Assumptions:
 ΔE – should be maximized
 ΔA – should be minimized
 Conclusion:
 R=ΔE/ΔA – the higher, the better
 Method:
 We estimate the R ratio for each matrix and set
matrices with the highest R from double to float
 This step is repeated until the accuracy loss is
lower than 1%
Set the
matrices with
the highest R
to float until
the accuracy
loss<1%
Sort them
decreasing
by R
Calculate
R=ΔE/ΔA
for each
matrix
The higher,
the better

16.  Precision: DOUBLE
 Diameter: 28.0
 L2 norm: 0.0746
 Diff. err.: 1.7503
 Phase err.: 0.7576
 Precision: MIXED
 Diameter: 28.0
 L2 norm: 0.0749
 Diff. err.: 1.7504
 Phase err.: 0.7576
16
Float group: x, xP, v3, h, v1P,v3P
Double group: v1, v2, v2P, cp, cn
Double

17. 17
Double Mixed The proposed
method was also
validated for the
other tests
 The difference
between L2 norms
for double and
mixed precision is
0.00001
 The phase is
44.2135 for both
cases

18.  Test: 512x512x512 – 3909 time steps
18
Double 1 335.48 44
Mixed 1 255.02 1.32 35 19.79
Double 32 27.52 71
Mixed 24 21.65 1.27 48 32.63
Conclusion: Energy consumption is reduced by 33%
Best
performance
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
1 6 11 16 21 26 31 36
Gflop/s
# of nodes
Double Mixed

19.  Test: 512x512x512 – 3909 time steps
19
Double 1/2 533.65 80
Mixed 1/2 352.18 1.51 53 34.00
Double 4/8 144.83 87
Mixed 4/8 96.04 1.51 57 33.66
Conclusion: Energy consumption is reduced by 33%
Best
performance
0
200
400
600
800
1000
1200
1400
1600
1800
2000
1 2 3 4
Gflop/s
# of GPUs – 2 GPUs per node
Double Mixed

20.  The developed implementation of MPDATA is very flexible and portable
 The proposed method allows us to automate the code adaptation even for a very large
number of possible configurations
 Mixed precision arithmetic allows us to reduce the energy consumption and execution
time
 It can be used in the real HPC platforms without special access to the machine
 It has an effect on the computation speed, data transfer, and scalability of the
application
 The proposed method allows us to reduce the energy consumption by 33% without loss
in accuracy
 It has also improved the performance by the factor of 1.27 for Piz Daint and 1.51 for
MICLAB in relation to double precision arithmetic
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21. We build Artificial Intelligence
software and integrate that into
products.
We port and optimize algorithms for
parallel, CPU+GPU architectures.
We design and optimize algorithms
for HPC supercomputers.
byteLAKE We are specialists in:
www.byteLAKE.com
Machine Learning
Deep Learning
Computer Vision
High Performance Computing
Heterogeneous Computing
Edge Computing
Our mission:
help industries transform for the era of Artificial Intelligence.
We combine business and academia. Our team consists of experts
schooled by Fortune 500 corporations as well as PhD researchers.

22. 22
Areas of Our Expertise
Computer Vision
Deep Learning
Machine Learning
Learning Optimization
AI for Edge Devices
HPC
Expertise Consultancy
Proof of Concept