OpenACC Tutorial - Profiling: Difference between revisions

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(Getting started with NVVP)
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<!--T:9-->
<!--T:9-->
What is so important about hotspots in the code?  
What is so important about hotspots in the code?  
Amdahl's law says that "Parallelizing the most time-consuming routines (i.e. the hotspots) will have the most impact".
The [https://en.wikipedia.org/wiki/Amdahl%27s_law Amdahl's law] says that
"Parallelizing the most time-consuming routines (i.e. the hotspots) will have the most impact".


== Build the Sample Code == <!--T:10-->
== Build the Sample Code == <!--T:10-->
For this example we will use code from this [https://github.com/calculquebec/cq-formation-openacc Git repository].
For the following example, we use a code from this [https://github.com/calculquebec/cq-formation-openacc Git repository].
Download the package and go to the '''cpp''' or '''f90''' directory.
You are invited to [https://github.com/calculquebec/cq-formation-openacc/archive/refs/heads/main.zip download and extract the package], and go to the <code>cpp</code> or the <code>f90</code> directory.
The object of this exercise is to compile and link the code, obtain an executable, and then profile it.
The object of this example is to compile and link the code, obtain an executable, and then profile its source code with a profiler.
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<!--T:4-->
Being pushed by [https://www.nvidia.com NVIDIA] through its
Being pushed by [https://www.cray.com/ Cray] and by [https://www.nvidia.com NVIDIA] through its
[https://www.pgroup.com/support/release_archive.php Portland Group] division until 2020 and now through its [https://developer.nvidia.com/hpc-sdk HPC SDK], as well as by
[https://www.pgroup.com/support/release_archive.php Portland Group] division until 2020 and now through its [https://developer.nvidia.com/hpc-sdk HPC SDK], these two lines of compilers offer the most advanced OpenACC support.
[https://www.cray.com/ Cray], these two lines of compilers offer the most advanced OpenACC support.


As for the [https://gcc.gnu.org/wiki/OpenACC GNU Compiler], since GCC version 6, the support for OpenACC 2.x kept improving.
<!--T:26-->
As for the [https://gcc.gnu.org/wiki/OpenACC GNU compilers], since GCC version 6, the support for OpenACC 2.x kept improving.
As of July 2022, GCC versions 10, 11 and 12 support OpenACC version 2.6.
As of July 2022, GCC versions 10, 11 and 12 support OpenACC version 2.6.


<!--T:5-->
<!--T:5-->
For the purpose of this tutorial, we use
For the purpose of this tutorial, we use the
[https://developer.nvidia.com/nvidia-hpc-sdk-releases version 22.7 of the NVIDIA HPC SDK].
[https://developer.nvidia.com/nvidia-hpc-sdk-releases NVIDIA HPC SDK], version 22.7.
We note that NVIDIA compilers are free for academic usage.  
Please note that NVIDIA compilers are free for academic usage.  
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<!--T:11-->
After the executable is created, we are going to profile that code.
Once the executable <code>cg.x</code> is created, we are going to profile its source code:
the profiler will measure function calls by executing and monitoring this program.
'''Important:''' this executable uses about 3GB of memory and one CPU core at near 100%.
Therefore, '''a proper test environment should have at least 4GB of available memory and at least two (2) CPU cores'''.
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For the purpose of this tutorial, we use two profilers as described below:  
For the purpose of this tutorial, we use two profilers:  
* NVIDIA Visual Profiler NVVP - a cross-platform analyzing tool for the codes written with OpenACC and CUDA C/C++ instructions.
* '''[https://docs.nvidia.com/cuda/profiler-users-guide/ NVIDIA <code>nvprof</code>]''' - a command line text-based profiler that can analyze non-GPU codes.
* NVPROF - a command line text-based version of the NVIDIA Visual Profiler.
* '''[[OpenACC_Tutorial_-_Adding_directives#NVIDIA_Visual_Profiler|NVIDIA Visual Profiler <code>nvvp</code>]]''' - a graphical cross-platform analyzing tool for the codes written with OpenACC and CUDA C/C++ instructions.
Since our previously built <code>cg.x</code> is not yet using the GPU, we will start the analysis with the <code>nvprof</code> profiler.
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=== NVIDIA Visual Profiler === <!--T:13-->


<!--T:14-->
=== NVIDIA <code>nvprof</code> Command Line Profiler === <!--T:15-->
One graphical profiler available for OpenACC applications is the
NVIDIA usually provides <code>nvprof</code> with its HPC SDK,
[https://developer.nvidia.com/nvidia-visual-profiler NVIDIA Visual Profiler (NVVP)].
but the proper version to use on our clusters is included with a CUDA module:
It's a cross-platform analyzing tool for code written with OpenACC and CUDA C/C++ instructions.
 
When [[Visualization/en#Remote_windows_with_X11-forwarding|X11 is forwarded to an X-Server]], or when using a [[VNC|Linux desktop environment]] (also via [[JupyterHub#Desktop|JupyterHub]]),
it is possible to launch the NVVP from a terminal:
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{{Command
{{Command
|module load cuda/11.7 java/1.8
|module load cuda/11.7
}}
{{Command
|nvvp
}}
}}
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[[File:Nvvp-pic0.png|thumbnail|300px|NVVP profiler|right]]
[[File:Nvvp-pic1.png|thumbnail|300px|Browse for the executable you want to profile|right]]


# After the NVVP startup window, you get prompted for a ''Workspace'' directory, which will be used for temporary files. Replace <code>home</code> with <code>scratch</code> in the suggested path. Then click ''OK''
<!--T:27-->
# Select ''File > New Session'', or click on the corresponding button in the toolbar
To profile a pure CPU executable, we need to add the arguments <code>--cpu-profiling on</code> to the command line:
# Click on the ''Browse'' button at the right of the ''File:'' path editor
## Browse to the <code>cq-formation-openacc/cpp</code> directory
## Select the executable <code>cg.x</code> that was compiled in a previous section. Then click ''OK''
# Click ''Finish'' to start profiling the executable.
 
=== NVIDIA NVPROF Command Line Profiler === <!--T:15-->
NVIDIA also provides a command line version called NVPROF, similar to GPU prof
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{{Command
{{Command
|nvprof --cpu-profiling on ./cg.x  
|nvprof --cpu-profiling on ./cg.x  
|result=
|result=
...
<Program output >
<Program output >
...
======== CPU profiling result (bottom up):
======== CPU profiling result (bottom up):
84.25% matvec(matrix const &, vector const &, vector const &)
Time(%)      Time  Name
84.25% main
83.54% 90.6757s  matvec(matrix const &, vector const &, vector const &)
9.50% waxpby(double, vector const &, double, vector const &, vector const &)
83.54% 90.6757s  {{!}} main
3.37% dot(vector const &, vector const &)
  7.94% 8.62146s  waxpby(double, vector const &, double, vector const &, vector const &)
2.76% allocate_3d_poisson_matrix(matrix&, int)
  7.94%  8.62146s  {{!}} main
2.76% main
  5.86% 6.36584s  dot(vector const &, vector const &)
0.11% __c_mset8
  5.86%  6.36584s  {{!}} main
0.03% munmap
  2.47% 2.67666s  allocate_3d_poisson_matrix(matrix&, int)
  0.03% free_matrix(matrix&)
  2.47% 2.67666s  {{!}} main
    0.03% main
  0.13% 140.35ms  initialize_vector(vector&, double)
  0.13% 140.35ms  {{!}} main
...
======== Data collected at 100Hz frequency
======== Data collected at 100Hz frequency
}}
}}
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<!--T:28-->
From the above output, the <code>matvec()</code> function is responsible for 83.5% of the execution time, and this function call can be found in the <code>main()</code> function.


== Compiler Feedback == <!--T:16-->
== Compiler Feedback == <!--T:16-->
Before working on the routine, we need to understand what the compiler is actually doing by asking ourselves the following questions:
Before working on the routine, we need to understand what the compiler is actually doing by asking ourselves the following questions:
* What optimizations were applied?  
* What optimizations were applied automatically by the compiler?  
* What prevented further optimizations?
* What prevented further optimizations?
* Can very minor modifications of the code affect performance?
* Can very minor modifications of the code affect performance?


<!--T:17-->
<!--T:17-->
The PGI compiler offers you a '''-Minfo''' flag with the following options:
The NVIDIA compiler offers a <code>-Minfo</code> flag with the following options:
* accel Print compiler operations related to the accelerator
* <code>all</code> - Print almost all types of compilation information, including:
* all – Print all compiler output
** <code>accel</code> - Print compiler operations related to the accelerator
* intensity Print loop intensity information
** <code>inline</code> - Print information about functions extracted and inlined
* ccff–Add information to the object files for use by tools
** <code>loop,mp,par,stdpar,vect</code> - Print various information about loop optimization and vectorization
* <code>intensity</code> - Print compute intensity information about loops
* (none) - If <code>-Minfo</code> is used without any option, it is the same as with the <code>all</code> option, but without the <code>inline</code> information


== How to Enable Compiler Feedback == <!--T:18-->
=== How to Enable Compiler Feedback === <!--T:18-->
* Edit the Makefile
* Edit the <code>Makefile</code>:
   CXX=nvc++
   CXX=nvc++
   CXXFLAGS=-fast -Minfo=all,intensity,ccff
   CXXFLAGS=-fast -Minfo=all,intensity
   LDFLAGS=${CXXFLAGS}
   LDFLAGS=${CXXFLAGS}
<!--T:29-->
* Rebuild
* Rebuild
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|make clean; make
|make clean; make
|result=
|result=
nvc++ -fast -Minfo=all,intensity,ccff   -c -o main.o main.cpp
...
nvc++ -fast -Minfo=all,intensity  -c -o main.o main.cpp
initialize_vector(vector &, double):
initialize_vector(vector &, double):
     20, include "vector.h"
     20, include "vector.h"
Line 166: Line 164:
           27, Intensity = 1.00
           27, Intensity = 1.00
               Generated vector simd code for the loop containing reductions
               Generated vector simd code for the loop containing reductions
              FMA (fused multiply-add) instruction(s) generated
          28, FMA (fused multiply-add) instruction(s) generated
waxpby(double, const vector &, double, const vector &, const vector &):
waxpby(double, const vector &, double, const vector &, const vector &):
     21, include "vector_functions.h"
     21, include "vector_functions.h"
Line 174: Line 172:
               Loop unrolled 2 times
               Loop unrolled 2 times
               FMA (fused multiply-add) instruction(s) generated
               FMA (fused multiply-add) instruction(s) generated
          40, FMA (fused multiply-add) instruction(s) generated
allocate_3d_poisson_matrix(matrix &, int):
allocate_3d_poisson_matrix(matrix &, int):
     22, include "matrix.h"
     22, include "matrix.h"
Line 181: Line 180:
               Loop not vectorized/parallelized: loop count too small
               Loop not vectorized/parallelized: loop count too small
           45, Intensity = 0.0
           45, Intensity = 0.0
              Loop unrolled 3 times (completely unrolled)
           57, Intensity = 0.0
           57, Intensity = 0.0
           59, Intensity = 0.0
           59, Intensity = 0.0
Line 187: Line 187:
     23, include "matrix_functions.h"
     23, include "matrix_functions.h"
           29, Intensity = (num_rows*((row_end-row_start)*        2))/(num_rows+(num_rows+(num_rows+((row_end-row_start)+(row_end-row_start)))))
           29, Intensity = (num_rows*((row_end-row_start)*        2))/(num_rows+(num_rows+(num_rows+((row_end-row_start)+(row_end-row_start)))))
              FMA (fused multiply-add) instruction(s) generated
           33, Intensity = 1.00
           33, Intensity = 1.00
               Loop not vectorized: non-stride-1 array reference
               Generated vector simd code for the loop containing reductions
              Loop not vectorized: mixed data types
          37, FMA (fused multiply-add) instruction(s) generated
              Loop unrolled 2 times
              FMA (fused multiply-add) instruction(s) generated
main:
main:
     38, allocate_3d_poisson_matrix(matrix &, int) inlined, size=41 (inline) file main.cpp (29)
     38, allocate_3d_poisson_matrix(matrix &, int) inlined, size=41 (inline) file main.cpp (29)
Line 200: Line 197:
               Loop not vectorized/parallelized: loop count too small
               Loop not vectorized/parallelized: loop count too small
           45, Intensity = 0.0
           45, Intensity = 0.0
              Loop unrolled 3 times (completely unrolled)
           57, Intensity = 0.0
           57, Intensity = 0.0
               Loop not fused: function call before adjacent loop
               Loop not fused: function call before adjacent loop
Line 211: Line 209:
     48, initialize_vector(vector &, double) inlined, size=5 (inline) file main.cpp (34)
     48, initialize_vector(vector &, double) inlined, size=5 (inline) file main.cpp (34)
           36, Intensity = 0.0
           36, Intensity = 0.0
               Loop not vectorized/parallelized: not countable
               Memory set idiom, loop replaced by call to __c_mset8
     49, initialize_vector(vector &, double) inlined, size=5 (inline) file main.cpp (34)
     49, initialize_vector(vector &, double) inlined, size=5 (inline) file main.cpp (34)
           36, Intensity = 0.0
           36, Intensity = 0.0
               Loop not vectorized/parallelized: not countable
               Memory set idiom, loop replaced by call to __c_mset8
     52, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
     52, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
           39, Intensity = 0.0
           39, Intensity = 0.0
Line 222: Line 220:
               Loop not fused: different loop trip count
               Loop not fused: different loop trip count
           33, Intensity = 1.00
           33, Intensity = 1.00
               Loop not vectorized: non-stride-1 array reference
               Generated vector simd code for the loop containing reductions
              Loop not vectorized: mixed data types
              Loop unrolled 2 times
     54, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
     54, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
           27, FMA (fused multiply-add) instruction(s) generated
           27, FMA (fused multiply-add) instruction(s) generated
           29, FMA (fused multiply-add) instruction(s) generated
           36, FMA (fused multiply-add) instruction(s) generated
          33, FMA (fused multiply-add) instruction(s) generated
           39, Intensity = 0.67
           39, Intensity = 0.67
               Loop not fused: different loop trip count
               Loop not fused: different loop trip count
Line 245: Line 240:
     65, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
     65, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
           27, Intensity = 1.00
           27, Intensity = 1.00
               Loop not fused: different loop trip count
               Loop not fused: different controlling conditions
               Generated vector simd code for the loop containing reductions
               Generated vector simd code for the loop containing reductions
     67, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
     67, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
Line 257: Line 252:
               Loop not fused: different loop trip count
               Loop not fused: different loop trip count
           33, Intensity = 1.00
           33, Intensity = 1.00
               Loop not vectorized: non-stride-1 array reference
               Generated vector simd code for the loop containing reductions
              Loop not vectorized: mixed data types
              Loop unrolled 2 times
     73, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
     73, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
           27, Intensity = 1.00
           27, Intensity = 1.00
Line 281: Line 274:
     91, free_vector(vector &) inlined, size=2 (inline) file main.cpp (29)
     91, free_vector(vector &) inlined, size=2 (inline) file main.cpp (29)
     92, free_matrix(matrix &) inlined, size=5 (inline) file main.cpp (73)
     92, free_matrix(matrix &) inlined, size=5 (inline) file main.cpp (73)
nvc++ main.o -o cg.x -fast -Minfo=all,intensity,ccff
}}
}}
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== Computational Intensity  == <!--T:19-->
=== Interpretation of the Compiler Feedback === <!--T:19-->
Computational Intensity of a loop is a measure of how much work is being done compared to memory operations.
The ''Computational Intensity'' of a loop is a measure of how much work is being done compared to memory operations.
Basically:


<!--T:20-->
<!--T:20-->
'''Computation Intensity = Compute Operations / Memory Operations'''
<math>\mbox{Computational Intensity} = \frac{\mbox{Compute Operations}}{\mbox{Memory Operations}}</math>


<!--T:21-->
<!--T:21-->
Computational Intensity of 1.0 or greater suggests that the loop might run well on a GPU.
In the compiler feedback, an <code>Intensity</code> <math>\ge</math> 1.0 suggests that the loop might run well on a GPU.


== Understanding the code  == <!--T:22-->
== Understanding the code  == <!--T:22-->
Let's look closely at the following code from <code>matrix_functions.h</code>:
Let's look closely at the main loop in the
[https://github.com/calculquebec/cq-formation-openacc/blob/main/cpp/matrix_functions.h#L29 <code>matvec()</code> function implemented in <code>matrix_functions.h</code>]:
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<syntaxhighlight lang="cpp" line highlight="1,5,10,12">
<syntaxhighlight lang="cpp" line start="29" highlight="1,5,10,12">
for(int i=0;i<num_rows;i++) {
  for(int i=0;i<num_rows;i++) {
  double sum=0;
    double sum=0;
  int row_start=row_offsets[i];
    int row_start=row_offsets[i];
  int row_end=row_offsets[i+1];
    int row_end=row_offsets[i+1];
  for(int j=row_start; j<row_end;j++) {
    for(int j=row_start; j<row_end;j++) {
    unsigned int Acol=cols[j];
      unsigned int Acol=cols[j];
    double Acoef=Acoefs[j];  
      double Acoef=Acoefs[j];  
    double xcoef=xcoefs[Acol];  
      double xcoef=xcoefs[Acol];  
    sum+=Acoef*xcoef;
      sum+=Acoef*xcoef;
    }
    ycoefs[i]=sum;
   }
   }
  ycoefs[i]=sum;
}
</syntaxhighlight>  
</syntaxhighlight>  
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Line 315: Line 309:
Given the code above, we search for data dependencies:
Given the code above, we search for data dependencies:
* Does one loop iteration affect other loop iterations?
* Does one loop iteration affect other loop iterations?
* Do loop iterations read from and write to different places in the same array?
** For example, when generating the '''[https://en.wikipedia.org/wiki/Fibonacci_number Fibonacci sequence]''', each new value depends on the previous two values. Therefore, efficient parallelism is very difficult to implement, if not impossible.
* Is sum a data dependency? No, it’s a reduction.
* Is the accumulation of values in <code>sum</code> a data dependency?
** No, it’s a '''[https://en.wikipedia.org/wiki/Reduction_operator reduction]'''! And modern compilers are good at optimizing such reductions.
* Do loop iterations read from and write to the same array, such that written values are used or overwritten in other iterations?
** Fortunately, that does not happen in the above code.


<!--T:25-->
<!--T:25-->

Latest revision as of 22:26, 20 December 2022

Other languages:


Learning objectives
  • Understand what a profiler is
  • Understand how to use the NVPROF profiler
  • Understand how the code is performing
  • Understand where to focus your time and rewrite most time consuming routines


Code profiling[edit]

Why would one need to profile code? Because it's the only way to understand:

  • Where time is being spent (hotspots)
  • How the code is performing
  • Where to focus your development time

What is so important about hotspots in the code? The Amdahl's law says that "Parallelizing the most time-consuming routines (i.e. the hotspots) will have the most impact".

Build the Sample Code[edit]

For the following example, we use a code from this Git repository. You are invited to download and extract the package, and go to the cpp or the f90 directory. The object of this example is to compile and link the code, obtain an executable, and then profile its source code with a profiler.


Which compiler ?

Being pushed by Cray and by NVIDIA through its Portland Group division until 2020 and now through its HPC SDK, these two lines of compilers offer the most advanced OpenACC support.

As for the GNU compilers, since GCC version 6, the support for OpenACC 2.x kept improving. As of July 2022, GCC versions 10, 11 and 12 support OpenACC version 2.6.

For the purpose of this tutorial, we use the NVIDIA HPC SDK, version 22.7. Please note that NVIDIA compilers are free for academic usage.


Question.png
[name@server ~]$ module load nvhpc/22.7
Lmod is automatically replacing "intel/2020.1.217" with "nvhpc/22.7".

The following have been reloaded with a version change:
  1) gcccore/.9.3.0 => gcccore/.11.3.0        3) openmpi/4.0.3 => openmpi/4.1.4
  2) libfabric/1.10.1 => libfabric/1.15.1     4) ucx/1.8.0 => ucx/1.12.1
Question.png
[name@server ~]$ make 
nvc++    -c -o main.o main.cpp
nvc++ main.o -o cg.x

Once the executable cg.x is created, we are going to profile its source code: the profiler will measure function calls by executing and monitoring this program. Important: this executable uses about 3GB of memory and one CPU core at near 100%. Therefore, a proper test environment should have at least 4GB of available memory and at least two (2) CPU cores.


Which profiler ?

For the purpose of this tutorial, we use two profilers:

  • NVIDIA nvprof - a command line text-based profiler that can analyze non-GPU codes.
  • NVIDIA Visual Profiler nvvp - a graphical cross-platform analyzing tool for the codes written with OpenACC and CUDA C/C++ instructions.

Since our previously built cg.x is not yet using the GPU, we will start the analysis with the nvprof profiler.


NVIDIA nvprof Command Line Profiler[edit]

NVIDIA usually provides nvprof with its HPC SDK, but the proper version to use on our clusters is included with a CUDA module:

Question.png
[name@server ~]$ module load cuda/11.7

To profile a pure CPU executable, we need to add the arguments --cpu-profiling on to the command line:

Question.png
[name@server ~]$ nvprof --cpu-profiling on ./cg.x 
...
<Program output >
...
======== CPU profiling result (bottom up):
Time(%)      Time  Name
 83.54%  90.6757s  matvec(matrix const &, vector const &, vector const &)
 83.54%  90.6757s  | main
  7.94%  8.62146s  waxpby(double, vector const &, double, vector const &, vector const &)
  7.94%  8.62146s  | main
  5.86%  6.36584s  dot(vector const &, vector const &)
  5.86%  6.36584s  | main
  2.47%  2.67666s  allocate_3d_poisson_matrix(matrix&, int)
  2.47%  2.67666s  | main
  0.13%  140.35ms  initialize_vector(vector&, double)
  0.13%  140.35ms  | main
...
======== Data collected at 100Hz frequency

From the above output, the matvec() function is responsible for 83.5% of the execution time, and this function call can be found in the main() function.

Compiler Feedback[edit]

Before working on the routine, we need to understand what the compiler is actually doing by asking ourselves the following questions:

  • What optimizations were applied automatically by the compiler?
  • What prevented further optimizations?
  • Can very minor modifications of the code affect performance?

The NVIDIA compiler offers a -Minfo flag with the following options:

  • all - Print almost all types of compilation information, including:
    • accel - Print compiler operations related to the accelerator
    • inline - Print information about functions extracted and inlined
    • loop,mp,par,stdpar,vect - Print various information about loop optimization and vectorization
  • intensity - Print compute intensity information about loops
  • (none) - If -Minfo is used without any option, it is the same as with the all option, but without the inline information

How to Enable Compiler Feedback[edit]

  • Edit the Makefile:
 CXX=nvc++
 CXXFLAGS=-fast -Minfo=all,intensity
 LDFLAGS=${CXXFLAGS}
  • Rebuild
Question.png
[name@server ~]$ make clean; make
...
nvc++ -fast -Minfo=all,intensity   -c -o main.o main.cpp
initialize_vector(vector &, double):
     20, include "vector.h"
          36, Intensity = 0.0
              Memory set idiom, loop replaced by call to __c_mset8
dot(const vector &, const vector &):
     21, include "vector_functions.h"
          27, Intensity = 1.00
              Generated vector simd code for the loop containing reductions
          28, FMA (fused multiply-add) instruction(s) generated
waxpby(double, const vector &, double, const vector &, const vector &):
     21, include "vector_functions.h"
          39, Intensity = 1.00
              Loop not vectorized: data dependency
              Generated vector simd code for the loop
              Loop unrolled 2 times
              FMA (fused multiply-add) instruction(s) generated
          40, FMA (fused multiply-add) instruction(s) generated
allocate_3d_poisson_matrix(matrix &, int):
     22, include "matrix.h"
          43, Intensity = 0.0
              Loop not fused: different loop trip count
          44, Intensity = 0.0
              Loop not vectorized/parallelized: loop count too small
          45, Intensity = 0.0
              Loop unrolled 3 times (completely unrolled)
          57, Intensity = 0.0
          59, Intensity = 0.0
              Loop not vectorized: data dependency
matvec(const matrix &, const vector &, const vector &):
     23, include "matrix_functions.h"
          29, Intensity = (num_rows*((row_end-row_start)*         2))/(num_rows+(num_rows+(num_rows+((row_end-row_start)+(row_end-row_start)))))
          33, Intensity = 1.00
              Generated vector simd code for the loop containing reductions
          37, FMA (fused multiply-add) instruction(s) generated
main:
     38, allocate_3d_poisson_matrix(matrix &, int) inlined, size=41 (inline) file main.cpp (29)
          43, Intensity = 0.0
              Loop not fused: different loop trip count
          44, Intensity = 0.0
              Loop not vectorized/parallelized: loop count too small
          45, Intensity = 0.0
              Loop unrolled 3 times (completely unrolled)
          57, Intensity = 0.0
              Loop not fused: function call before adjacent loop
          59, Intensity = 0.0
              Loop not vectorized: data dependency
     42, allocate_vector(vector &, unsigned int) inlined, size=3 (inline) file main.cpp (24)
     43, allocate_vector(vector &, unsigned int) inlined, size=3 (inline) file main.cpp (24)
     44, allocate_vector(vector &, unsigned int) inlined, size=3 (inline) file main.cpp (24)
     45, allocate_vector(vector &, unsigned int) inlined, size=3 (inline) file main.cpp (24)
     46, allocate_vector(vector &, unsigned int) inlined, size=3 (inline) file main.cpp (24)
     48, initialize_vector(vector &, double) inlined, size=5 (inline) file main.cpp (34)
          36, Intensity = 0.0
              Memory set idiom, loop replaced by call to __c_mset8
     49, initialize_vector(vector &, double) inlined, size=5 (inline) file main.cpp (34)
          36, Intensity = 0.0
              Memory set idiom, loop replaced by call to __c_mset8
     52, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
          39, Intensity = 0.0
              Memory copy idiom, loop replaced by call to __c_mcopy8
     53, matvec(const matrix &, const vector &, const vector &) inlined, size=19 (inline) file main.cpp (20)
          29, Intensity = [symbolic], and not printable, try the -Mpfi -Mpfo options
              Loop not fused: different loop trip count
          33, Intensity = 1.00
              Generated vector simd code for the loop containing reductions
     54, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
          27, FMA (fused multiply-add) instruction(s) generated
          36, FMA (fused multiply-add) instruction(s) generated
          39, Intensity = 0.67
              Loop not fused: different loop trip count
              Loop not vectorized: data dependency
              Generated vector simd code for the loop
              Loop unrolled 4 times
              FMA (fused multiply-add) instruction(s) generated
     56, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
          27, Intensity = 1.00
              Loop not fused: function call before adjacent loop
              Generated vector simd code for the loop containing reductions
     61, Intensity = 0.0
     62, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
          39, Intensity = 0.0
              Memory copy idiom, loop replaced by call to __c_mcopy8
     65, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
          27, Intensity = 1.00
              Loop not fused: different controlling conditions
              Generated vector simd code for the loop containing reductions
     67, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
          39, Intensity = 0.67
              Loop not fused: different loop trip count
              Loop not vectorized: data dependency
              Generated vector simd code for the loop
              Loop unrolled 4 times
     72, matvec(const matrix &, const vector &, const vector &) inlined, size=19 (inline) file main.cpp (20)
          29, Intensity = [symbolic], and not printable, try the -Mpfi -Mpfo options
              Loop not fused: different loop trip count
          33, Intensity = 1.00
              Generated vector simd code for the loop containing reductions
     73, dot(const vector &, const vector &) inlined, size=9 (inline) file main.cpp (21)
          27, Intensity = 1.00
              Loop not fused: different loop trip count
              Generated vector simd code for the loop containing reductions
     77, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
          39, Intensity = 0.67
              Loop not fused: different loop trip count
              Loop not vectorized: data dependency
              Generated vector simd code for the loop
              Loop unrolled 4 times
     78, waxpby(double, const vector &, double, const vector &, const vector &) inlined, size=10 (inline) file main.cpp (33)
          39, Intensity = 0.67
              Loop not fused: function call before adjacent loop
              Loop not vectorized: data dependency
              Generated vector simd code for the loop
              Loop unrolled 4 times
     88, free_vector(vector &) inlined, size=2 (inline) file main.cpp (29)
     89, free_vector(vector &) inlined, size=2 (inline) file main.cpp (29)
     90, free_vector(vector &) inlined, size=2 (inline) file main.cpp (29)
     91, free_vector(vector &) inlined, size=2 (inline) file main.cpp (29)
     92, free_matrix(matrix &) inlined, size=5 (inline) file main.cpp (73)

Interpretation of the Compiler Feedback[edit]

The Computational Intensity of a loop is a measure of how much work is being done compared to memory operations. Basically:

In the compiler feedback, an Intensity 1.0 suggests that the loop might run well on a GPU.

Understanding the code[edit]

Let's look closely at the main loop in the matvec() function implemented in matrix_functions.h:

  for(int i=0;i<num_rows;i++) {
    double sum=0;
    int row_start=row_offsets[i];
    int row_end=row_offsets[i+1];
    for(int j=row_start; j<row_end;j++) {
      unsigned int Acol=cols[j];
      double Acoef=Acoefs[j]; 
      double xcoef=xcoefs[Acol]; 
      sum+=Acoef*xcoef;
    }
    ycoefs[i]=sum;
  }

Given the code above, we search for data dependencies:

  • Does one loop iteration affect other loop iterations?
    • For example, when generating the Fibonacci sequence, each new value depends on the previous two values. Therefore, efficient parallelism is very difficult to implement, if not impossible.
  • Is the accumulation of values in sum a data dependency?
    • No, it’s a reduction! And modern compilers are good at optimizing such reductions.
  • Do loop iterations read from and write to the same array, such that written values are used or overwritten in other iterations?
    • Fortunately, that does not happen in the above code.

Now that the code analysis is done, we are ready to add directives to the compiler.

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