SESH framework: A Space Exploration Framework for GPU

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SESH framework: A Space Exploration Framework
for GPU Application and Hardware Codesign
Joo Hwan Lee
Jiayuan Meng
Hyesoon Kim
School of Computer Science
Georgia Institute of Technology
Atlanta, GA, USA
[email protected]
Leadership Computing Facility
Argonne National Laboratory
Argonne, IL, USA
[email protected]
School of Computer Science
Georgia Institute of Technology
Atlanta, GA, USA
[email protected]
Abstract—Graphics processing units (GPUs) have become
increasingly popular accelerators in supercomputers, and this
trend is likely to continue. With its disruptive architecture
and a variety of optimization options, it is often desirable to
understand the dynamics between potential application transformations and potential hardware features when designing future
GPUs for scientific workloads. However, current codesign efforts
have been limited to manual investigation of benchmarks on
microarchitecture simulators, which is labor-intensive and timeconsuming. As a result, system designers can explore only a small
portion of the design space. In this paper, we propose SESH
framework, a model-driven codesign framework for GPU, that is
able to automatically search the design space by simultaneously
exploring prospective application and hardware implementations
and evaluate potential software-hardware interactions.
I.
I NTRODUCTION
As demonstrated by the supercomputers Titan and Tianhe1A, graphics processing units (GPUs) have become integral
components in supercomputers. This trend is likely to continue,
as more workloads are exploiting data-level parallelism and
their problem sizes increase.
A major challenge in designing future GPU-enabled systems for scientific computing is to gain a holistic understanding
about the dynamics between the workloads and the hardware. Conventionally built for graphics applications, GPUs
have various hardware features that can boost performance if
carefully managed; however, GPU hardware designers may not
be sufficiently informed about scientific workloads to evaluate
specialized hardware features. On the other hand, since GPU
architectures embrace massive parallelism and limited L1
storage per thread, legacy codes must be redesigned in order
to be ported to GPUs. Even codes for earlier GPU generations
may have to be recoded in order to fully exploit new GPU
architectures. As a result, an increasing effort has been made
in codesigning the application and the hardware.
In a typical codesign effort, a set of benchmarks is proposed
by application developers and is then manually studied by
hardware designers in order to understand the potential. However, such a process is labor-intensive and time-consuming. In
addition, several factors challenge system designers’ endeavors
to explore the design space. First, the number of hardware
configurations is exploding as the complexity of the hardware
increases. Second, the solution has to meet several design
constraints such as area and power. Third, benchmarks are
often provided in a specific implementation, yet one often
needs to attempt tens of transformations in order to fully
understand the performance potential of a specific hardware
configuration. Fourth, evaluating the performance of a particular implementation on a future hardware may take significant
time using simulators. Fifth, the current performance tools
(e.g., simulators, hardware models, profilers) investigate either
hardware or applications in a separate manner, treating the
other as a black box and therefore, offer limited insights for
codesign.
To efficiently explore the design space and provide firstorder insights, we propose SESH, a model-driven framework
that automatically searches the design space by simultaneously
exploring prospective application and hardware implementations and evaluate potential software-hardware interactions.
SESH recommends the optimal combination of application
optimizations and hardware implementations according to
user-defined objectives with respect to performance, area, and
power. The technical contributions of the SESH framework are
as follows.
1)
2)
3)
It evaluates various software optimization effects and
hardware configurations using decoupled workload
models and hardware models.
It integrates GPU’s performance, area, and power
models into a single framework.
It automatically proposes optimal hardware configurations given multi facet metrics in aspects of performance, area, and power.
We evaluate our work using a set of representative scientific
workloads. A large design space is explored that considers
both application transformations and hardware configurations.
We evaluate potential solutions using various metrics including
performance, area efficiency, and energy consumption. Then,
we summarize the overall insights gained from such space
exploration.
The paper is organized as follows. In Section II, we
provide an overview of our work. In Section III, we introduce the integrated hardware models for power and area.
Section IV describes the space exploration process. Evaluation
methodology and results are described in Sections V and VI,
respectively. After the related work is discussed in Section VII,
we conclude.
II.
OVERVIEW AND BACKGROUND
The SESH framework is a codesign tool for GPU system
designers and performance engineers. It recommends the optimal combination of hardware configurations and application
implementations. Different from existing performance models
or architecture simulators, SESH considers how applications
may transform and adapt to potential hardware architectures.
A. Overall Framework
Source Code Workload Input The SESH framework is built on top of existing performance modeling frameworks. We integrated GROPHECY [2]
as the GPU workload modeling and transformation engine. We
also adopted area and power models from previous work on
projection engine. Below we provide a brief description about
them.
User Effort Code Skeletons SESH Framework Hardware Modeling & Workload Modeling & Transforma:on Engine Transforma:on Engine Engine Projec:on Energy Performance Area Projec:on Projec:on Projec:on Fig. 1.
B. GROPHECY-Based Code Transformation Engine
Op:mal Transforma:on & Hardware Framework Overview.
Source Code of Matrix Mul3plica3on (C = A*B) 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
float A[N][K], B[K][M];
float C[N][M];
int i, j, k;
// nested for loop
for(i=0; i<N; ++i)
{
for(j=0; j<M; ++j)
{
float sum = 0;
for(k=0; k<K; ++k)
{
sum+=A[i][k]*B[k][j];
}
C[i][j] = sum;
}
}
Code Skeleton 1. 
2. 
3. 
4. 
5. 
6. 
7. 
8. 
9. 
10. 
11. 
12. 
13. 
14. 
15. 
16. 
17. 
18. 
19. 
20. 
float A[N][K], B[K][M]
float C[N][M]
/* the loop space */
forall i=0:N, j=0:M
{
/* computation w/t
* instruction count
*/
comp 1
/* reduction loop */
reduce k = 0:K {
/* load */
ld A[i][k]
ld B[k][j]
comp 3
}
comp 5
/* store */
st C[i][j]
}
Fig. 2. A pedagogical example of a code skeleton in the case of matrix
multiplication. A code skeleton is used as the input to our framework.
As Figure 1 shows, the major components of the SESH
framework include (i) a workload modeling and transformation
engine, (ii) a hardware modeling and transformation engine,
and (iii) a projection engine. Using the framework involves
the following work flow:
1)
2)
3)
automatically proposing potential application transformations and hardware configurations.
SESH projects the energy consumption and execution
time for each combination of transformations and
hardware configurations, and recommends the best
solution according to user-specified metrics, without
manual coding or lengthy simulations. Such metrics
can be a combination of power, area, and performance. For example, one metric can be “given an
area budget, what would be the most power efficient
hardware considering potential transformations?”.
The user abstracts high level characteristics of the
source code into a code skeleton that summarizes
control flows, potential parallelism, instruction mix,
and data access patterns. An example code skeleton
is shown in Figure 2. This step can be automated by
SKOPE [1], and the user can amend the output code
skeleton with additional notions such as for_all
or reduction.
Given the code skeleton and the specified power and
area constraints, SESH explores the design space by
GROPHECY [2], a GPU code transformation framework,
has been proposed to explore various transformations and to
estimate the GPU performance of a CPU kernel. Provided with
a code skeleton, GROPHECY is able to transform the code
skeleton to mimic various optimization strategies. Transformations explored include spatial and temporal loop tiling, loop
fusion, unrolling, shared memory optimizations, and memory
request coalescing. GROPHECY then analytically computes
the characteristics of each transformation. The resulting characteristics are used as inputs to a GPU performance model
to project the performance of the corresponding transformation. The best achievable performance and the transformations
necessary to reach that performance are then projected.
GROPHECY, however, relies on the user to specify a
particular hardware configuration. It does not explore the
hardware design space to study how hardware configurations
would affect the performance or efficiency of various code
transformations. In this work, we extend GROPHECY with parameterized power and area models so that one can integrate it
into a larger framework that explores hardware configurations
together with code transformations.
C. Hardware Models
We utilize the performance model from the work of Sim et
al. [3]. We make it tunable to reflect different GPU architecture
specifications. The tunable parameters are Register file entry
count, SIMD width, SFU width, L1D/SHMEM size and LLC
cache size. The model takes several workload characteristics
as its inputs, including the instruction mix and the number of
memory operations.
We utilize the work by Lim et al. [4] for chip-level
area and power models. They model GPU power based on
McPAT [5] and an energy introspection interface (EI) [6] and
integrate the power-modeling functionality in MacSim [7], a
trace-driven and cycle-level GPU simulator. McPAT enables
users to configure a microarchitecture by rearranging circuitlevel models. EI creates pseudo components that are linked
to McPAT’s circuit-level models and utilizes access counters
to calculate the power consumption of each component. We
use this model to estimate the power value for the baseline
architecture configuration. Then we adopt simple heuristics
to estimate the power consumption for different hardware
configurations.
E XPLORATORY, M ULTI FACET H ARDWARE M ODEL
In order to explore the hardware design space and evaluate
tradeoffs, the SESH framework integrates performance, power
and area models, all parameterized and tunable according to
the hardware configuration. In this section, we first describe
the process to prepare the reference models about the NVIDIA
GTX 580 architecture. These models include power and area
models for chip. We then integrate these models and parameterize them so that they can reflect changes in hardware
configurations.
The variation in power consumption caused by thermal
changes is not modeled for the purpose of simplicity. As
measured in [8], we assume a constant temperature of 340 K
(67 ◦ C) in the power model, considering that this operationtime temperature is higher than the code-state temperature of
57 ◦ C [8].
52.7% 40.0% 26.3% 80.0% 0.6% 0.1% 69.9% 60.0% 40.0% 20.0% 12.0% 1.8% 1.8% _A
LU
s EX
_F
PU
s EX
_S
FU
EX
_L
D/
ST
Ex
ec
uD
on
M
M
L1
U
D/
SH
M
E
M
Co
ns
tC
ac
Te
he
xt
ur
eC
ac
he
4.6% 1.5% 0.2% 0.2% EX
0.0% 1.3% 0.5% 1.5% 2.2% 2.6% Fig. 4. Area consumption for all non-DRAM components(top) and for SMprivate components(bottom).
For the area model, we utilize the area outcome from
energy introspection integrated with MacSim [4]. The energy
introspection interface in MacSim utilizes area size to calculate
power. It also estimates area sizes for different hardware
configurations. we use the area outcomes that are based on
NVIDIA GTX 580.
Figure 4 (top) shows the area breakdown of GTX 580 based
on our area model. The total area consumption of the chip is
3588.0 mm2 . LLC (61.7%) accounts for the majority of the
chip area. Figure 4 (bottom) shows the breakdown of the area
for SM-private components. The main processing part, 32 SPs
(EX ALUs and EX FPUs), occupy the largest portion of the
area (69.9% and 2.6%, respectively). The L1D / SHMEM is
the second largest module (12.0%). SFU (4.6%) and RF (2.2%)
also account for a large portion of area consumption.
3.7% 0.0% 0.0% 6.5% 0.3% 0.5% RF
_A LU
EX s _F
PU
EX s _S
EX FU _L
D
E x /S T
ec
uC
on
L1 MM
D/
SH U Co MEM
ns
Te tCa
c
xt
ur he eC
ac
he
LL
C M
C No
C 0.1% 1.2% 0.2% C. Integrated, Tunable Hardware Model
Power consumption for non-DRAM components.
Figure 3 shows how much total power is consumed by each
component according our model. The GPU’s on-chip power is
decomposed into two categories; SM-private components and
knobtarget
knobbaseline
knobtarget
= P owerbaseline ×
knobbaseline
Areatarget = Areabaseline ×
P owertarget
Fig. 3.
1.7% 0.5% 0.1% 0.1% 4.5% 0.7% 0.7% RF
_A LU
EX s _F
PU
EX s _S
EX FU _L
D
E x /S T
ec
uD
on
L1 MM
D/
SH U Co MEM
ns
Te tCa
c
xt
ur he eC
ac
he
LL
C M
C No
C 0.5% 0.2% 0.6% 0.8% 1.0% EX
0.0% 17.6% EX
Fe
tc
De h co
Sc de he
du
le
0.0% 0.3% 1.4% 0.7% 40.0% RF
To estimate the static power for a baseline architecture of
NVIDIA GTX 580, we collect power statistics from a detailed
power simulator [4]. The Sepia benchmark [9] is used as
an example input for the simulation. Note that the choice
of the benchmark does not affect significantly the value of
static power. In Sepia’s on-chip power consumption, the static
power consumes 106.0 W while the dynamic power consumes
50.0 W. The DRAM power is 52.0 W in Sepia, although
it is usually more than 90.0 W in other benchmarks. As a
result, the dynamic power accounts for 24.0% of Sepia’s the
total power consumption of the chip and DRAM. Taking the
dynamic power into account will be included in our future
work.
11.1% 3.7% 61.7% 60.0% Fe
tc
De h co
Sc de he
du
le
To get reference values for chip-level power consumption,
we use the detailed power simulator in Section II-C. As
Hong and Kim [8] showed, the GPU power consumption is
not significantly affected by the dynamic power consumption
except the DRAM power values. Furthermore, the static power
is often the dominant factor for on-chip power consumption.
Hence, to get the first-order approximation of the GPU power
model, we focus on the static power only.
20.0% 80.0% 20.0% A. The Reference Model for Chip-Level Power
60.0% B. The Reference Model for Chip-Level Area
Fe
tc
h De
co
de
Sc
he
du
le
III.
SM-shared components. The total on-chip power consumption
is 156.0 W. SM-private components accounts for 93 % (144.7
W) of the overall power, and shared components between SMs
account for 7% (11.4 W) of the overall power. From all the
SM-private components we model EX ALUs and EX FPUs
consume the most power (52.7% and 11.1%, respectively).
SFU (17.6%), LLC (6.5%), and RF (3.7%) also account for
large portions of the overall power consumption.
(1)
(2)
To estimate how changes in hardware configurations affect
the overall power consumption, we employ a heuristic that
the per-component power consumption and area scales linearly
TABLE I.
H ARDWARE COMPONENTS THAT ARE MODELED AS
TUNABLE KNOBS .
Stage
KNOB
RF
ALU
FPU
SFU
L1D/SHMEM
LLC
TABLE II.
per second on each SM is referred to as DRAM transaction
intensity, whose value is M ax T rans Intensity under the
aforementioned theoretical condition.
Default(NVIDIA GTX 580)
Per-SM
Register file entry count
SIMD width
SIMD width
SFU width
L1D size + SHMEM size
Shared
L2 Cache size
32,768 / SM
32 / SM
32 / SM
4 / SM
64KB / SM
T rans Intensity =
Shared
Stage
Fetch,
Decode,
Schedule,
Execution(except ALU, FPU, SFU),
MMU, Const$, Tex$
1 MemCon, 1 NoC, 1 DRAM
with the size and the number of components (e.g., doubling
the shared memory size would double its power consumption
and also area). Given a target hardware’s configuration, we
can compute the per-component area and power according to
Equations (1) and (2), respectively, where knob refers to
the size or number of the component in the corresponding
architecture. The baseline data is collected as described in
Sections III-A and III-B. The per-component metrics are
then aggregated to project the system-level area and power
consumption.
According to our analysis in Figures 3 and 4, the major
components consuming power and area include the register
files, ALUs, FPUs, SFUs, L1 cache size, and the last level
cache size. The quantities of these components become tunable
variables, or knobs, in the integrated model. Table I lists the
knobs and the value of knobbaseline in Equations (1) and
(2). The area and power consumption of other components
are approximated as constant values obtained from modeling
NVIDIA GTX 580. These components are summarized in
Table II.
D. DRAM Power Model
DRAM power depends on memory access patterns; the
number of DRAM row buffer hits/misses can affect power consumption noticeably. However, these numbers can be obtained
only from the detailed simulation, which often takes several
hours for each configuration (100s of software optimizations ×
10s of hardware configurations easily create 1000s of different
configurations). To mitigate the overhead, we use a simple
empirical approach to compute the first-order estimation of
DRAM power consumption values.
PDRAM = M axDynP ×
T rans Intensity
+ StatP
M ax T rans Intensity
(4)
In this work, the actual DRAM transaction intensity,
T rans Intensity, is approximated by Equation (4). The total
number of DRAM transactions per SM (#DRAM Accesses)
and the execution time in seconds (Exec time) are estimated
values given by the performance model.
768KB
H ARDWARE COMPONENTS THAT ARE MODELED WITH
CONSTANT AREA AND POWER CONSUMPTION .
Category
Per-SM(w/ fixed number of SMs)
#DRAM Accesses
Exec time
In order to construct Equation (3) as a function of
the workload characteristics, the values of StatP and
M axDynP
M AX T rans Intensity need to be obtained as constant coefficients. We therefore use the power simulator to obtain
the DRAM power for SVM and Sepia in the Merge benchmarks [9] and solve for the values of these two coefficients.
Equation (5) represents the resulting DRAM model.
PDRAM = α × T rans Intensity + β
where α = 1.6 × 10
−6
IV.
The total DRAM power (PDRAM ) is computed by adding
up the static power (StatP ) and dynamic power [8]. The
dynamic power is computed as a fraction of the maximum
dynamic power (M axDynP ), which can only be reached
in the theoretical condition where every instruction generates
a DRAM transaction. The number of DRAM transactions
and β = 24.4
S PACE E XPLORATION
Application transformations and hardware configurations
pose a design space that is daunting to explore. First, they
are inter-related; different hardware configurations may prefer different application transformations. Second, there are a
gigantic number of options. In our current framework, we
explore each of them independently and then calculate which
combination yields the desired solution. Note that this process
is made possible largely because of the fast evaluation enabled
by modeling.
The application transformations explored include spatial
and temporal loop tiling, unrolling, shared memory optimizations, and memory request coalescing. The hardware configurations explored include SIMD width and shared memory size,
which play significant roles in performance, area, and power.
We plan to explore more dimensions in our future work.
To compare different solutions, we utilize multiple objective functions that represent different design goals. Those
objective functions include the followings.
1)
2)
3)
Shortest execution time
Minimal energy consumption
Largest performance per area
V.
(3)
(5)
M ETHODOLOGY
A. Workloads
The benchmarks used for our evaluation and their key
properties are summarized in Table III. HotSpot and SRAD are
applications from the Rodinia benchmark suite [10]. Stassuij is
extracted from a DOE INCITE application performing Monte
Carlo calculations to study light nuclei [11], [12]. It has two
kernels: IspinEx and SpinFlap. We separately evaluate each
kernel of Stassuij and also evaluate both kernels together. The
TABLE III.
Benchmark
HotSpot
SRAD
IspinEx
SpinFlap
Stassuij
W ORKLOAD PROPERTIES
Key Properties
Structured grid. Iterative, self-dependent kernels. A deep dependency chain among dependent kernels
Structured grid. Data dependency involves
multiple arrays; each points to different producer iterations
Sparse linear algebra, A X B
Irregular data exchange similar to spectral
methods
Nested loops. Dependent parallel loops with
different shapes. Dependency involves indirectly accessed arrays
Input Size
1024 X 1024
4096 X 4096
A : 132 X 132,
B : 132 X 2048
132 X 2048
-
sizes of matrices in Stassuij are according to real input data.
To reduce the space of code transformations to explore, for
each benchmark we set a fixed thread block size large enough
to saturate wide SIMD.
HotSpot: HotSpot is an ordinary differential equation solver
used in simulating microarchitecture temperature. It has a
stencil computation kernel with structured grid. Kernels are executed iteratively, and each iteration consumes a neighborhood
of array elements. As a result, each iteration depends on the
previous one. Programmers can utilize shared memory(ShM)
by caching neighborhood data for inter-thread data sharing.
Folding, which assigns multiple tasks to one thread, improves
data reuse by allowing a thread to process more neighborhoodgathering tasks. Fusing loop partitions across several iterations
can be applied to achieve better locality and reduce global halo
exchanges. We also provide a hint that indicates only one of
the arrays used in double buffering is the necessary output for
the fused kernel. In our experiments, we fuse two dependent
iterations and use a 16 × 16 partition for the consumer loop.
The thread block size is set to 16 × 16.
SRAD: SRAD performs spectral removal anisotropic diffusion to an image. It has two kernels: the first generates
diffusion coefficients and the second updates the image. We
use a 16 × 16 thread block size and indicate the output array
that needs to be committed.
IspinEx: IspinEx is a sparse matrix multiplication kernel
which multiplies a 132 × 132 sparse matrix of real numbers
with a 132 × 2048 dense matrix of complex numbers. We
provide a hint that the average number of nonzero elements
in one row of the sparse matrix is 14 in order to estimate
the overall workload size. Because the numbers of elements
associated with different rows may vary. we force a thread
to process all elements in columns to balance the workload
among threads. We treat the real part and imaginal part of the
complex number as individual numbers and employ a 1 × 64
thread block size in our evaluation. Due to irregularity in sparse
data accesses, we provide a hint about the average degree of
coalescing, which is obtained from offline characterization of
the input data.
SpinFlap: SpinFlap exchanges matrix elements in groups
of four. Each group is scattered in a butterfly pattern in the
same row, similar to spectral methods. Which columns are to
be grouped together is determined by values in another array.
SpinFlap is a memory-bounded kernel. By utilizing shared
memory, programmers can expect performance improvement.
There is data reuse by multiple threads on the matrix, which are
used for indirect indices for other matrices. The performance
can also be improved by folding. Performance is highly
dependent on the degree of coalescing, and it varies according
to values of indirect indices. To assess the degree of coalescing,
we profiled the average data stride of indirect indices and
provide this hint to the framework. We assume a 12 × 16
thread block size with no folding.
Stassuij(Fused): Fusion increases the reuse in shared
memory. But since data dependency caused by indirect indices
in SpinFlap requires IspinEx to be partitioned accordingly,
the loop index in IspinEx now becomes a value pointed by
indirect accesses in the fused kernel, introducing irregular
strides that can become un-coalesced memory accesses. We
assume a thread block size of 16 × 4 × 2 and provide a hint
that indicates the output array.
B. Evaluation Metric
To study how application performance is affected by code
transformations and architectural changes, we utilize metrics
from previous work [3] to understand the potential optimization benefits and the performance bottlenecks.
1)
2)
3)
4)
B serial : Benefits of removing serialization effects
such as synchronization and resource contention.
B itilp : Benefits of increasing inter-thread
instruction-level
parallelism
(ITILP).
ITILP
represents global ILP (ILP among warps).
B memlp : Benefits of increasing memory-level
parallelism (MLP)
B f p : Benefits of improving computing efficiency.
Computing efficiency represents the ratio of the floating point instructions over the total instructions.
VI.
E VALUATION
While we have explored a design space with both code
transformations and hardware configurations, we present our
results according to SIMD widths and shared memory sizes
in order to shed more light on hardware designs. We model
64 transformations for HotSpot, 64, 128 transformations for
two kernels of SRAD, 576, 1728 and 2816 transformations
for IspinEx, SpinFlap and Stassuij(Fused) respectively.
A. SIMD Width
We evaluate different SIMD widths from 16 to 128.
Figure 5 represents the execution time, energy consumption, possible benefits and performance per area for optimal
transformation for HotSpot with increasing SIMD width. The
performance-optimal SIMD width is 64 and the optimal SIMD
width for minimal energy consumption and maximal performance per area is 32, which is the same as for NVIDIA GTX
580. The reason is that the increased inefficiency in power
and area is bigger than the benefit of shorter execution time,
even though minimal execution time helps reduce the energy
consumption in general. Performance increases from 16 to 64
but decreases from 64 to 128. The application becomes more
memory bound with increased SIMD width, and the benefit
of less computation time becomes smaller, which we can see
from increasing B memlp.
B_fp: B_serial: B_memlp: energy: 0.5 0.4 0.3 0.2 0.1 0 cycles: 1500000 1000000 500000 cycle count energy (J) B_i6lp: 0 16 32(perf/area, 64(cycle, dram energy energy op6mal) op6mal) 128 1 def ispinex ( ) {
2
...
3
f o r a l l j = 0 : n t , i r = 0 : n s ∗2 {
4
...
5
r e d u c e ( f l o a t , +) n = 0 : a v g j n t d t {
6
...
7
ld cr [ njp ] [ i r ]
/ / D i f f e r e n t on 289 & 370
8
...
9
}
10
...
11
}
12 }
1/(cycle*area) (1/mm2) perf_per_area: 5E-­‐10 Fig. 7.
4E-­‐10 3E-­‐10 Comparison of transformations 289 & 370 for IspinEx.
TABLE IV.
O PTIMAL SIMD WIDTH REGARDING MINIMAL EXECUTION
TIME , MINIMAL ENERGY CONSUMPTION AND MAXIMAL PERFORMANCE
PER AREA .
2E-­‐10 1E-­‐10 0 16 32(perf/area, energy op7mal) 64(cycle, dram energy op7mal) 128 SIMD Width Benchmark
HotSpot
SRAD(first)
SRAD(second)
IspinEx
SpinFlap
Stassuij
IspinEx : SIMD
Fig. 5. Execution time, energy consumption, possible benefits and performance per area for optimal transformation for HotSpot on increasing SIMD
width.
2000000
cycle count
289 cycles_comp:
1500000
289 cycles_mem:
370 cycles_comp:
1000000
Energy
32
32
16
16
16
16
Perf/Area
32
32
16
16
128
32
depending on the degree of loop tiling, loop fusion, unrolling,
shared memory optimizations, and memory request coalescing.
Figure 7 compares transformations 289 and 370 for IspinEx.
Those two have same code structure; the only difference is the
decision of which loads to be cached or not. Transformation
370 utilizes shared memory for the load ld cr[njp][ir], while
transformation 289 doesn’t. The difference between transformations 513 and 1210 for SpinFlap is also which loads utilize
shared memory or not.
SpinFlap : SIMD
370 cycles_mem:
500000
289 cycles:
370 cycles:
0
16
32
64
128
300000
cycle count
Performance
64
32
32
128
128
32
250000
513 cycles_comp:
200000
513 cycles_mem:
150000
1210 cycles_comp:
100000
1210 cycles_mem:
513 cycles:
50000
1210 cycles:
0
16
32
64
128
Fig. 6. Comparison between optimal transformation with increasing SIMD
width for IspinEx(top) and SpinFlap(bottom).
For HotSpot, SRAD, and Stassuij, the optimal transformation remains the same regardless of SIMD width and
objective function. However, depending on SIMD width, optimal transformation changes from 289 (16, 32, 64) to 370
(128) for IspinEx and from 513 (16, 32) to 1210 (64, 128)
for SpinFlap. Figures 6 compares the optimal transformation
with increasing SIMD width for IspinEx and SpinFlap. The
optimal transformation on a narrow SIMD width is selected
because it incurs less computation, even though it incurs more
memory traffic due to un-coalesced access on a wide SIMD
width than optimal transformation on a wide SIMD width.
However, the application becomes more memory bound with
increased SIMD width, therefore reducing the benefit of less
computation.
The transformation ID we use in this paper can be different
The optimal SIMD width is different depending on workload objective functions. Table IV represents optimal SIMD
width for HotSpot, SRAD, IspinEx, SpinFlap and Stassuij
regarding minimal execution time, minimal energy consumption and maximal performance per area. We also find strong
correlation between minimal energy consumption and largest
performance per area. Except for SpinFlap and Stassuij, the
optimal SIMD width for minimal energy consumption and the
one for largest performance per area are the same.
Considering source code transformation or not changes
the optimal SIMD width for SpinFlap. Table V compares
the optimal SIMD width for SpinFlap when using optimal
transformation on NVIDIA GTX 580 or using optimal transformation on each SIMD width. The optimal SIMD width
for performance and performance per area is 128 and the
energy optimal SIMD width is 16 when we consider source
code transformation. However, 16 is the optimal SIMD width
for all objective functions when we do not consider source
code transformation and use the optimal transformation on
NVIDIA GTX 580 instead. Figure 8 compares the execution
time, energy consumption and possible benefits for SpinFlap
TABLE V.
O PTIMAL SIMD WIDTH FOR S PIN F LAP USING FIXED
TRANSFORMATION OR OPTIMAL TRANSFORMATION ON EACH SIMD
WIDTH .
Benchmark
Fixed
Variable
Performance
16
128
Energy
16
16
Perf/Area
16
128
with increasing SIMD width considering source code transformation or not.
TABLE VI.
N UMBER OF TRANSFORMATIONS AVAILABLE FOR
I SPIN E X , S PIN F LAP, AND S TASSUIJ DEPENDING ON SHARED MEMORY
SIZE .
Stassuij(Fusion) : Memory Bound
cycles: 300000 1
250000 200000 150000 100000 0.1
50000 0 B_i9lp: B_fp: 32 64 B_serial: 128(perf/area, cycle, dram 0.01
energy op2mal) B_memlp: energy: 0.1 0.08 0.06 0.04 0.02 0 32 64 energy_dram:
128(dram energy op9mal) In summary, increasing SIMD width helps performance.
But the benefit of large SIMD width degrades because of
increased inefficiency in power and area, and the application
becomes more memory bound with increased SIMD width.
The optimal SIMD width is depends on workload objective
functions, with strong correlation between minimal energy
consumption and largest performance per area. The optimal
transformation changes depend on SIMD width for IspinEx
and SpinFlap. Considering source code transformation or not
changes the optimal SIMD width for SpinFlap.
128 KB
288
1728
2816
per SM for optimal transformations
for these applications is
2000000
already less than 16 KB. Figure 9 represents the performance
0
perTransformation
area for optimal transformation
for HotSpot on increasing
shared memory size.
Shared_memory_per_SM(KB):
100
80
60
40
20
0
Fig. 8. Execution time, energy consumption and possible benefits for optimal
transformation for SpinFlap with increasing SIMD width: (top) considering
source code transformation; (bottom) using fixed transformation.
64 KB
192
1304
2240
4000000
cycles: 300000 250000 200000 150000 100000 50000 0 16(cycle, perf/
area, energy op9mal) Benchmark
16 KB
48 KB
IspinEx
120
192
energy:
cycles:
SpinFlap
432
1304
Stassuij
2240 6000000
2240
Transformation
Fig. 10.
Shared memory requirement for transformations for Stassuij.
For HotSpot and SRAD, none of the transformations are
disabled even when the shared memory size per SM is reduced
to 16 KB. Such is not the case for IspinEx, SpinFlap and
Stassuij. Figure 10 presents the shared memory requirement for
all transformations for Stassuij. Some transformation require
less than 20 KB of shared memory, but other transformations
require more than 80 KB of shared memory. Therefore the
number of valid transformations is different depending on
the shared memory size. Table VI presents the number of
transformations available for IspinEx, SpinFlap and Stassuij
depending on shared memory size.
cycles: B. Shared Memory Size
cycles_comp: cycles_mem: Shared_memory_per_SM: GPU’s shared memory is a software-managed L1 storage
on an SM. A larger shared memory would enable new transformations with more aggressive caching. We evaluate shared
memory sizes from 16 KB to 128 KB. The values of other
parameters remain constant.
cycle count 1500000 128 112 96 80 64 48 32 16 0 1000000 500000 0 16(281) 48,64(289) cycles_comp: cycles_mem: SHMEM size (KB) energy: SHMEM size (KB)
B_memlp: 0.05 0.04 0.03 0.02 0.01 0 16(energy op2mal) energy (J) B_serial: cycle count B_fp: cycle count energy (J) B_i2lp: 128(317) Shared_memory_per_SM: 500000 16(perf/area, cycle, dram_energy, energy op=mal) 48 64 128 144 128 112 96 80 64 48 32 16 0 400000 300000 200000 100000 0 16, 48, 64(513) Fig. 9. Performance per area for optimal transformation for HotSpot with
increasing shared memory size.
The optimal transformation for HotSpot, SRAD and Stassuij and their performance remain the same regardless of
shared memory size. The reason is that shared memory usage
SHMEM size (KB) cycles: 4.5E-­‐10 4.4E-­‐10 4.3E-­‐10 4.2E-­‐10 4.1E-­‐10 4E-­‐10 cycle count 1/(cycle*area) (1/mm2) perf_per_area: 128(756) Fig. 11. Comparison between the optimal transformations when increasing
shared memory size for IspinEx(top) and SpinFlap(bottom).
The optimal transformation for Stassuij remains the same
regardless of shared memory size since shared memory usage
per SM for the optimal transformation is less than 9 KB. However, the optimal transformation changes depending on shared
memory size for IspinEx and SpinFlap. New transformations
become available as we increase the shared memory size. The
optimal transformation changes from 281 (16 KB) to 289 (48,
64 KB), 317 (128 KB) for IspinEx, and it changes from 513
(16, 48, 64 KB) to 756 (128 KB) for SpinFlap. Figure 11
compares the optimal transformation with increasing shared
memory size for IspinEx and SpinFlap. The difference between
those transformations is which loads utilize shared memory.
C. Discussion
The lessons learned from our model-driven space exploration is summarized below.
1)
2)
B_serial: B_memlp: energy: energy (J) 0.19 0.185 0.18 0.175 0.17 16 B_i6lp: energy (J) cycles: 1400000 1200000 1000000 800000 600000 400000 200000 0 48 B_fp: B_serial: 64 B_memlp: cycle count B_fp: 128(perf/area, cycle, dram energy, energy op<mal) energy: 300000 0.045 250000 200000 0.044 150000 0.043 100000 0.042 3)
cycles: 0.046 cycle count B_i<lp: 0.195 50000 0.041 0 16(perf/area, energy op6mal) 48 64 128(cycle, dram energy op6mal) Fig. 12.
Execution time, energy consumption and possible benefits for
optimal transformation on increasing shared memory size for IspinEx(top)
and SpinFlap(bottom).
Figure 12 represents the execution time and energy consumption for the optimal transformations of IspinEx and SpinFlap with increasing shared memory size. When we consider
code transformations, the optimal shared memory size for all
objective function for IspinEx is 128 KB. Without considering
transformations however, the optimal shared memory size is 48
KB. For SpinFlap, the optimal shared memory size for energy
and performance per area is 16 KB and the performanceoptimal shared memory size is 128 KB when we consider
source code transformation. Without considering transformations, the optimal shared memory size remains 16 KB for all
objective functions.
In summary, shared memory sizes determine the number of
possible transformations in terms of how the shared memory is
used. For IspinEx, SpinFlap and Stassuij, some transformations
are disabled because of limitation of shared memory size.
These applications prefer either small shared memory or very
large shared memory, as we can see in Figure 10. For IspinEx
and SpinFlap, the optimal transformation changes depending
on shared memory size since new transformations become
available with increased shared memory size. Considering
source code transformations or not changes the optimal shared
memory size for IspinEx and SpinFlap.
4)
5)
For a given hardware, the code transformation with
minimal execution time often leads to minimal energy
consumption as well. This can be observed from
Figure 13, which represents execution time and energy consumption of possible transformations of each
application on NVIDIA GTX 580.
The optimal hardware configuration depends on the
objective function. In general, performance increases
with more resources (wider SIMD width or bigger
shared memory size). However, the performance benefit of more resources may be outweighed by the cost
of more resources in terms of energy or area. Therefore, the SIMD width and shared memory size that
are optimal for energy consumption and performance
per area are smaller than those for performance.
We also observe that the SIMD width and shared
memory size that minimize energy consumption also
maximize performance per area.
The optimal transformation can differ across hardware configurations. The variation in hardware configuration has two effects on code transformations: it
shifts the performance bottleneck, or it enables/disables potential transformations because of resource
availability. In the examples of IspinEx and SpinFlap, a computation-intensive transformation becomes memory-bound with wide SIMD; a new transformation that requires large L1 storage is enabled
when the shared memory size increases.
The optimal hardware configuration varies according to whether code transformations are considered.
For example, when searching for the performanceoptimal SIMD width for SpinFlap, the legacy implementation would suggest a SIMD width of 16,
while the performance-optimal SIMD width is 128
if transformations are considered and would perform
2.6 × better. The optimal shared memory size would
also change for IspinEx and SpinFlap by taking
transformations into account.
In order to gain performance, it is generally better
to increase the SIMD width rather than the shared
memory size. Larger SIMD width increases performance at the expense of area and power consumption.
Larger shared memory size does not have a significant
impact on performance until it can accommodate a
larger working set, therefore enabling a new transformation; however, we found that a shared memory
size of 48 KB is already able to accommodate a
reasonably sized working set in most cases. This
coincides with GPU’s hardware design trends from
Tesla [13] to Fermi [14] and Kepler [15]. Moreover,
we found that energy-optimal shared memory size for
all evaluated benchmarks is less than 48 KB, which
is the value for current Fermi architecture.
Our work can be improved to enable broader space exploration in less time. A main challenge in space exploration is
the large number of possible transformations and architectural
parameters. Instead of brute-force exploration, we plan to
energy_dram: energy: 10000 0.1 0.01 energy_dram: Transforma-on energy: 10 100000000 1 Transforma:on cycles: 1 energy (J) 10 20000000 15000000 10000000 5000000 0 Transforma7on 1 cycles: 20000000 2 10000000 1 0 Transforma8on energy_dram: cycles: 10000 0.1 energy: 3 energy: 1 100000000 1 0.01 energy_dram: cycles: 0 cycles: 6000000 4000000 0.1 0.01 cycle count energy: 2000000 Transforma:on cycle count 0 Transforma;on 5 4 3 2 1 0 energy (J) 1000000 energy (J) 2000000 cycle count 0.5 cycle count energy (J) 3000000 0 energy (J) energy_dram: 4000000 energy (J) cycles: cycle count energy: cycle count energy_dram: 1 0 Fig. 13. Execution time and energy consumption of possible transformations of each application on NVIDIA GTX 580. From top to bottom, HotSpot, SRAD
(first) SRAD (second), IspinEx, SpinFlap and Stassuij (Fused).
build a feedback mechanism to probe the space judiciously.
For example, if an application is memory bound, the SESH
framework can try transformations that result in fewer memory
operations but more computation, or hardware configurations
with large shared memory and smaller SIMD width.
VII.
R ELATED WORK
Multiple software frameworks are proposed to help GPU
programming [16], [17]. Workload characterization studies [18], [19] and parallel programming models including
PRAM, BSP, CTA and LogP are also relevant to our work [20],
[21]. These techniques do not explore the hardware design
space.
To the best of our knowledge, there has been no previous
work to study the relationships between GPU code transformation and power reduction. Valluri et al. [22] performed
quantitative study of the effect of the optimizations by DEC
Alpha’s cc compiler. Brandolese et al. [23] explored source
code transformation in terms of energy consumption using the
SimpleScalar simulator.
Modeling power consumption of CPUs has been widely
studied. Joseph’s technique relies on performance counters [24]. Bellosa et al. [25] also used performance counters
in order to determine the energy consumption and estimate
the temperature for a dynamic thermal management. Wu et
al. [26] proposed utilizing phasic behavior of programs in
order to build a linear system of equations for component unit
power estimation. Peddersen and Parameswaran [27] proposed
a processor that estimates its own power/energy consumption
at runtime. CAMP [28] used the linear regression model to
estimate activity factor and power; it provides insights that
relate microarchitectural statistics to activity factor and power.
Jacobson et al. [29] built various levels of abstract models
and proposed a systematic way to find a utilization metric for
estimating power numbers and a scaling method to evaluate
new microarchitecture. Czechowski and Vuduc [30] studied
relationship between architectural features and algorithm characteristics. They proposed a modeling framework that can be
used for tradeoff analysis of performance and power.
While architectural studies and performance improvements
with GPUs have been explored widely, power modeling of
GPUs has received little attention. A few works use functional simulator for power modeling. Wang [31] extended
GPGPUSim with Wattch and Orion to compute GPU power.
PowerRed [32], a modular architectural power estimation
framework, combined both analytical and empirical models;
they also modeled interconnect power dissipation by employing area cost. A few GPU power modeling works use a
statistical linear regression method using empirical data. Ma et
al. [33] dynamically predicted the runtime power of NVIDIA
GeForce 8800 GT using recorded power data and a trained
statistical model. Nagasaka et al. [34] used the linear regression
method by collecting the information about the application
from performance counters. Tree-based random forest method
was used on the works by Chen et al. [35] and by Zhang
et al. [36]. Since those works are based on empirical data
obtained from existing hardware, they do not provide insights
in terms of space exploration.
Simulators have been widely used to search the hardware
design space. Generic algorithms and regression have been
proposed to reduce the search space by learning from a
relatively small number of simulations [37]. Our work extends
their work by considering code transformations, integrating
area and power estimations, and employing models instead
of simulations. Nevertheless, their learning-based approach is
complementary to our approach and may help SESH framework prune the space as well.
VIII.
C ONCLUSIONS
We propose the SESH framework, a model-driven framework that automatically searches the design space by simultaneously exploring prospective application and hardware
implementations and evaluate potential software-hardware interactions. It recommends the optimal combination of application optimizations and hardware implementations according
to user-defined objectives with respect to performance, area,
and power. We explored the GPU hardware design space with
different SIMD widths and shared memory sizes, and we
evaluated each design point using four benchmarks, each with
hundreds of transformations. The evaluation criteria include
performance, energy consumption, and performance per area.
Several codesign lessons were learned from the framework,
and our findings point to the importance of considering code
transformations in designing future GPU hardware.
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