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HPC OpenMP Lab 3

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README.md
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@ -12,4 +12,4 @@ This repo contains the exercises and the tutorials used for Unimore's HPC class
The exercises related to OpenMP programming model can be found in the folder `openmp`. Here the list of currectly available classes: The exercises related to OpenMP programming model can be found in the folder `openmp`. Here the list of currectly available classes:
- `openmp\lab1`: OpenMP basics: *parallel*, *for-loop*, *sections*, and *tasking*. - `openmp\lab1`: OpenMP basics: *parallel*, *for-loop*, *sections*, and *tasking*.
- `openmp\lab2`: OpenMP Advanced: *reduction*, *tasking*, *optimizations*. - `openmp\lab2`: OpenMP Advanced: *reduction*, *tasking*, *optimizations*.
- `openmp\lab3`: OpenMP 4.x+: *Accelerator Model (targeting: Nvidia GP-GPU)*

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openmp/lab3/.solutions/jacobi-omp1.c Normal file
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/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file jacobi.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief This code solves the steady state heat equation on a rectangular region.
* This code solves the steady state heat equation on a rectangular region.
* The sequential version of this program needs approximately
* 18/epsilon iterations to complete.
* The physical region, and the boundary conditions, are suggested
* by this diagram;
* W = 0
* +------------------+
* | |
* W = 100 | | W = 100
* | |
* +------------------+
* W = 100
* The region is covered with a grid of M by N nodes, and an N by N
* array W is used to record the temperature. The correspondence between
* array indices and locations in the region is suggested by giving the
* indices of the four corners:
* I = 0
* [0][0]-------------[0][N-1]
* | |
* J = 0 | | J = N-1
* | |
* [M-1][0]-----------[M-1][N-1]
* I = M-1
* The steady state solution to the discrete heat equation satisfies the
* following condition at an interior grid point:
* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* where "Central" is the index of the grid point, "North" is the index
* of its immediate neighbor to the "north", and so on.
*
* Given an approximate solution of the steady state heat equation, a
* "better" solution is given by replacing each interior point by the
* average of its 4 neighbors - in other words, by using the condition
* as an ASSIGNMENT statement:
* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* If this process is repeated often enough, the difference between successive
* estimates of the solution will go to zero.
* This program carries out such an iteration, using a tolerance specified by
* the user, and writes the final estimate of the solution to a file that can
* be used for graphic processing.
* icensing:
* This code is distributed under the GNU LGPL license.
* odified:
* 18 October 2011
* uthor:
* Original C version by Michael Quinn.
* This C version by John Burkardt.
* eference:
* Michael Quinn,
* Parallel Programming in C with MPI and OpenMP,
* McGraw-Hill, 2004,
* ISBN13: 978-0071232654,
* LC: QA76.73.C15.Q55.
* ocal parameters:
* Local, double DIFF, the norm of the change in the solution from one iteration
* to the next.
* Local, double MEAN, the average of the boundary values, used to initialize
* the values of the solution in the interior.
* Local, double U[M][N], the solution at the previous iteration.
* Local, double W[M][N], the solution computed at the latest iteration.
*
*
* @see https://en.wikipedia.org/wiki/Jacobi_method
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include "utils.h"
static int N;
static int MAX_ITERATIONS;
static int SEED;
static double CONVERGENCE_THRESHOLD;
static FILE *data;
#define SEPARATOR "------------------------------------\n"
// Return the current time in seconds since the Epoch
double get_timestamp();
// Parse command line arguments to set solver parameters
void parse_arguments(int argc, char *argv[]);
// Run the Jacobi solver
// Returns the number of iterations performed
int run(double *restrict A, double *restrict xtmp)
{
int iter = 0, iterations_print = 1;
double err = 0.0;
do
{
err = 0.0;
#pragma omp target map(to \
: A [0:N * N]) map(from \
: xtmp [0:N * N]) map(tofrom \
: err)
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
err = fmax(err, fabs(xtmp[i * N + j] - A[i * N + j]));
}
}
#pragma omp target map(to \
: xtmp [0:N * N]) map(from \
: A [0:N * N])
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A[i * N + j] = xtmp[i * N + j];
}
}
iter++;
#ifdef DEBUG
if (iter == iterations_print)
{
printf(" %8d %f\n", iter, err);
iterations_print = 2 * iterations_print;
}
#endif
} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
return iter;
}
int main(int argc, char *argv[])
{
parse_arguments(argc, argv);
double *A = malloc(N * N * sizeof(double));
double *xtmp = malloc(N * N * sizeof(double));
printf(SEPARATOR);
printf("Matrix size: %dx%d\n", N, N);
printf("Maximum iterations: %d\n", MAX_ITERATIONS);
printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
printf(SEPARATOR);
for (int ii = 0; ii < N; ii++)
{
for (int jj = 0; jj < N; jj++)
{
double f;
fread(&f, sizeof(double), 1, data);
A[ii * N + jj] = f;
}
}
// Run Jacobi solver
start_timer();
int itr = run(A, xtmp);
stop_timer();
printf("Iterations = %d\n", itr);
printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
if (itr == MAX_ITERATIONS)
printf("WARNING: solution did not converge\n");
printf(SEPARATOR);
free(A);
free(xtmp);
fclose(data);
return 0;
}
int parse_int(const char *str)
{
char *next;
int value = strtoul(str, &next, 10);
return strlen(next) ? -1 : value;
}
double parse_double(const char *str)
{
char *next;
double value = strtod(str, &next);
return strlen(next) ? -1 : value;
}
void parse_arguments(int argc, char *argv[])
{
// Set default values
N = 500;
MAX_ITERATIONS = 2000;
CONVERGENCE_THRESHOLD = 0.001;
SEED = 0;
for (int i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
{
if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
{
printf("Invalid convergence threshold\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
{
if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
{
printf("Invalid number of iterations\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
{
if (++i >= argc || (N = parse_int(argv[i])) < 0)
{
printf("Invalid matrix order\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
{
printf("\n");
printf("Usage: ./jacobi [OPTIONS]\n\n");
printf("Options:\n");
printf(" -h --help Print this message\n");
printf(" -c --convergence C Set convergence threshold\n");
printf(" -i --iterations I Set maximum number of iterations\n");
printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
printf("\n");
exit(0);
}
else
{
printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
exit(1);
}
}
if (N == 1000)
data = fopen("data/jacobi-1000.bin", "rb");
else if (N == 500)
data = fopen("data/jacobi-500.bin", "rb");
else
{
printf("Invalid matrix order\n");
exit(1);
}
}

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openmp/lab3/.solutions/jacobi-omp2.c Normal file
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/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file jacobi.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief This code solves the steady state heat equation on a rectangular region.
* This code solves the steady state heat equation on a rectangular region.
* The sequential version of this program needs approximately
* 18/epsilon iterations to complete.
* The physical region, and the boundary conditions, are suggested
* by this diagram;
* W = 0
* +------------------+
* | |
* W = 100 | | W = 100
* | |
* +------------------+
* W = 100
* The region is covered with a grid of M by N nodes, and an N by N
* array W is used to record the temperature. The correspondence between
* array indices and locations in the region is suggested by giving the
* indices of the four corners:
* I = 0
* [0][0]-------------[0][N-1]
* | |
* J = 0 | | J = N-1
* | |
* [M-1][0]-----------[M-1][N-1]
* I = M-1
* The steady state solution to the discrete heat equation satisfies the
* following condition at an interior grid point:
* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* where "Central" is the index of the grid point, "North" is the index
* of its immediate neighbor to the "north", and so on.
*
* Given an approximate solution of the steady state heat equation, a
* "better" solution is given by replacing each interior point by the
* average of its 4 neighbors - in other words, by using the condition
* as an ASSIGNMENT statement:
* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* If this process is repeated often enough, the difference between successive
* estimates of the solution will go to zero.
* This program carries out such an iteration, using a tolerance specified by
* the user, and writes the final estimate of the solution to a file that can
* be used for graphic processing.
* icensing:
* This code is distributed under the GNU LGPL license.
* odified:
* 18 October 2011
* uthor:
* Original C version by Michael Quinn.
* This C version by John Burkardt.
* eference:
* Michael Quinn,
* Parallel Programming in C with MPI and OpenMP,
* McGraw-Hill, 2004,
* ISBN13: 978-0071232654,
* LC: QA76.73.C15.Q55.
* ocal parameters:
* Local, double DIFF, the norm of the change in the solution from one iteration
* to the next.
* Local, double MEAN, the average of the boundary values, used to initialize
* the values of the solution in the interior.
* Local, double U[M][N], the solution at the previous iteration.
* Local, double W[M][N], the solution computed at the latest iteration.
*
*
* @see https://en.wikipedia.org/wiki/Jacobi_method
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include "utils.h"
static int N;
static int MAX_ITERATIONS;
static int SEED;
static double CONVERGENCE_THRESHOLD;
static FILE *data;
#define SEPARATOR "------------------------------------\n"
// Return the current time in seconds since the Epoch
double get_timestamp();
// Parse command line arguments to set solver parameters
void parse_arguments(int argc, char *argv[]);
// Run the Jacobi solver
// Returns the number of iterations performed
int run(double *restrict A, double *restrict xtmp)
{
int iter = 0, iterations_print = 1;
double err = 0.0;
do
{
err = 0.0;
#pragma omp target map(to \
: A [0:N * N]) map(from \
: xtmp [0:N * N]) map(tofrom \
: err)
#pragma omp teams distribute parallel for reduction(max \
: err)
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
err = fmax(err, fabs(xtmp[i * N + j] - A[i * N + j]));
}
}
#pragma omp target map(to \
: xtmp [0:N * N]) map(from \
: A [0:N * N])
#pragma omp teams distribute parallel for
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A[i * N + j] = xtmp[i * N + j];
}
}
iter++;
#ifdef DEBUG
if (iter == iterations_print)
{
printf(" %8d %f\n", iter, err);
iterations_print = 2 * iterations_print;
}
#endif
} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
return iter;
}
int main(int argc, char *argv[])
{
parse_arguments(argc, argv);
double *A = malloc(N * N * sizeof(double));
double *xtmp = malloc(N * N * sizeof(double));
printf(SEPARATOR);
printf("Matrix size: %dx%d\n", N, N);
printf("Maximum iterations: %d\n", MAX_ITERATIONS);
printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
printf(SEPARATOR);
for (int ii = 0; ii < N; ii++)
{
for (int jj = 0; jj < N; jj++)
{
double f;
fread(&f, sizeof(double), 1, data);
A[ii * N + jj] = f;
}
}
// Run Jacobi solver
start_timer();
int itr = run(A, xtmp);
stop_timer();
printf("Iterations = %d\n", itr);
printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
if (itr == MAX_ITERATIONS)
printf("WARNING: solution did not converge\n");
printf(SEPARATOR);
free(A);
free(xtmp);
fclose(data);
return 0;
}
int parse_int(const char *str)
{
char *next;
int value = strtoul(str, &next, 10);
return strlen(next) ? -1 : value;
}
double parse_double(const char *str)
{
char *next;
double value = strtod(str, &next);
return strlen(next) ? -1 : value;
}
void parse_arguments(int argc, char *argv[])
{
// Set default values
N = 500;
MAX_ITERATIONS = 2000;
CONVERGENCE_THRESHOLD = 0.001;
SEED = 0;
for (int i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
{
if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
{
printf("Invalid convergence threshold\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
{
if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
{
printf("Invalid number of iterations\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
{
if (++i >= argc || (N = parse_int(argv[i])) < 0)
{
printf("Invalid matrix order\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
{
printf("\n");
printf("Usage: ./jacobi [OPTIONS]\n\n");
printf("Options:\n");
printf(" -h --help Print this message\n");
printf(" -c --convergence C Set convergence threshold\n");
printf(" -i --iterations I Set maximum number of iterations\n");
printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
printf("\n");
exit(0);
}
else
{
printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
exit(1);
}
}
if (N == 1000)
data = fopen("data/jacobi-1000.bin", "rb");
else if (N == 500)
data = fopen("data/jacobi-500.bin", "rb");
else
{
printf("Invalid matrix order\n");
exit(1);
}
}

293
openmp/lab3/.solutions/jacobi-omp3.c Normal file
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@ -0,0 +1,293 @@
/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file jacobi.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief This code solves the steady state heat equation on a rectangular region.
* This code solves the steady state heat equation on a rectangular region.
* The sequential version of this program needs approximately
* 18/epsilon iterations to complete.
* The physical region, and the boundary conditions, are suggested
* by this diagram;
* W = 0
* +------------------+
* | |
* W = 100 | | W = 100
* | |
* +------------------+
* W = 100
* The region is covered with a grid of M by N nodes, and an N by N
* array W is used to record the temperature. The correspondence between
* array indices and locations in the region is suggested by giving the
* indices of the four corners:
* I = 0
* [0][0]-------------[0][N-1]
* | |
* J = 0 | | J = N-1
* | |
* [M-1][0]-----------[M-1][N-1]
* I = M-1
* The steady state solution to the discrete heat equation satisfies the
* following condition at an interior grid point:
* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* where "Central" is the index of the grid point, "North" is the index
* of its immediate neighbor to the "north", and so on.
*
* Given an approximate solution of the steady state heat equation, a
* "better" solution is given by replacing each interior point by the
* average of its 4 neighbors - in other words, by using the condition
* as an ASSIGNMENT statement:
* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* If this process is repeated often enough, the difference between successive
* estimates of the solution will go to zero.
* This program carries out such an iteration, using a tolerance specified by
* the user, and writes the final estimate of the solution to a file that can
* be used for graphic processing.
* icensing:
* This code is distributed under the GNU LGPL license.
* odified:
* 18 October 2011
* uthor:
* Original C version by Michael Quinn.
* This C version by John Burkardt.
* eference:
* Michael Quinn,
* Parallel Programming in C with MPI and OpenMP,
* McGraw-Hill, 2004,
* ISBN13: 978-0071232654,
* LC: QA76.73.C15.Q55.
* ocal parameters:
* Local, double DIFF, the norm of the change in the solution from one iteration
* to the next.
* Local, double MEAN, the average of the boundary values, used to initialize
* the values of the solution in the interior.
* Local, double U[M][N], the solution at the previous iteration.
* Local, double W[M][N], the solution computed at the latest iteration.
*
*
* @see https://en.wikipedia.org/wiki/Jacobi_method
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include "utils.h"
static int N;
static int MAX_ITERATIONS;
static int SEED;
static double CONVERGENCE_THRESHOLD;
static FILE *data;
#define SEPARATOR "------------------------------------\n"
// Return the current time in seconds since the Epoch
double get_timestamp();
// Parse command line arguments to set solver parameters
void parse_arguments(int argc, char *argv[]);
// Run the Jacobi solver
// Returns the number of iterations performed
int run(double *restrict A, double *restrict xtmp)
{
int iter = 0, iterations_print = 1;
double err = 0.0;
do
{
err = 0.0;
#pragma omp target data map(to \
: A [0:N * N]) map(from \
: xtmp [0:N * N]) map(tofrom \
: err)
#pragma omp target teams num_teams(N / NTHREADS_GPU) thread_limit(NTHREADS_GPU) map(to \
: A [0:N * N]) map(from \
: xtmp [0:N * N]) map(tofrom \
: err)
#pragma omp distribute parallel for collapse(2) num_threads(NTHREADS_GPU) dist_schedule(static, NTHREADS_GPU) reduction(max \
: err) schedule(static, 1)
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
err = fmax(err, fabs(xtmp[i * N + j] - A[i * N + j]));
}
}
#pragma omp target data map(from \
: A [0:N * N]) map(to \
: xtmp [0:N * N])
#pragma omp target teams num_teams(N / NTHREADS_GPU) thread_limit(NTHREADS_GPU) map(from \
: A [0:N * N]) map(to \
: xtmp [0:N * N])
#pragma omp distribute parallel for collapse(2) num_threads(NTHREADS_GPU) dist_schedule(static, NTHREADS_GPU) schedule(static, 1)
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A[i * N + j] = xtmp[i * N + j];
}
}
iter++;
#ifdef DEBUG
if (iter == iterations_print)
{
printf(" %8d %f\n", iter, err);
iterations_print = 2 * iterations_print;
}
#endif
} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
return iter;
}
int main(int argc, char *argv[])
{
parse_arguments(argc, argv);
double *A = malloc(N * N * sizeof(double));
double *xtmp = malloc(N * N * sizeof(double));
printf(SEPARATOR);
printf("Matrix size: %dx%d\n", N, N);
printf("Maximum iterations: %d\n", MAX_ITERATIONS);
printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
printf(SEPARATOR);
for (int ii = 0; ii < N; ii++)
{
for (int jj = 0; jj < N; jj++)
{
double f;
fread(&f, sizeof(double), 1, data);
A[ii * N + jj] = f;
}
}
// Run Jacobi solver
start_timer();
int itr = run(A, xtmp);
stop_timer();
printf("Iterations = %d\n", itr);
printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
if (itr == MAX_ITERATIONS)
printf("WARNING: solution did not converge\n");
printf(SEPARATOR);
free(A);
free(xtmp);
fclose(data);
return 0;
}
int parse_int(const char *str)
{
char *next;
int value = strtoul(str, &next, 10);
return strlen(next) ? -1 : value;
}
double parse_double(const char *str)
{
char *next;
double value = strtod(str, &next);
return strlen(next) ? -1 : value;
}
void parse_arguments(int argc, char *argv[])
{
// Set default values
N = 500;
MAX_ITERATIONS = 2000;
CONVERGENCE_THRESHOLD = 0.001;
SEED = 0;
for (int i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
{
if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
{
printf("Invalid convergence threshold\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
{
if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
{
printf("Invalid number of iterations\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
{
if (++i >= argc || (N = parse_int(argv[i])) < 0)
{
printf("Invalid matrix order\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
{
printf("\n");
printf("Usage: ./jacobi [OPTIONS]\n\n");
printf("Options:\n");
printf(" -h --help Print this message\n");
printf(" -c --convergence C Set convergence threshold\n");
printf(" -i --iterations I Set maximum number of iterations\n");
printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
printf("\n");
exit(0);
}
else
{
printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
exit(1);
}
}
if (N == 1000)
data = fopen("data/jacobi-1000.bin", "rb");
else if (N == 500)
data = fopen("data/jacobi-500.bin", "rb");
else
{
printf("Invalid matrix order\n");
exit(1);
}
}

292
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@ -0,0 +1,292 @@
/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file jacobi.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief This code solves the steady state heat equation on a rectangular region.
* This code solves the steady state heat equation on a rectangular region.
* The sequential version of this program needs approximately
* 18/epsilon iterations to complete.
* The physical region, and the boundary conditions, are suggested
* by this diagram;
* W = 0
* +------------------+
* | |
* W = 100 | | W = 100
* | |
* +------------------+
* W = 100
* The region is covered with a grid of M by N nodes, and an N by N
* array W is used to record the temperature. The correspondence between
* array indices and locations in the region is suggested by giving the
* indices of the four corners:
* I = 0
* [0][0]-------------[0][N-1]
* | |
* J = 0 | | J = N-1
* | |
* [M-1][0]-----------[M-1][N-1]
* I = M-1
* The steady state solution to the discrete heat equation satisfies the
* following condition at an interior grid point:
* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* where "Central" is the index of the grid point, "North" is the index
* of its immediate neighbor to the "north", and so on.
*
* Given an approximate solution of the steady state heat equation, a
* "better" solution is given by replacing each interior point by the
* average of its 4 neighbors - in other words, by using the condition
* as an ASSIGNMENT statement:
* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* If this process is repeated often enough, the difference between successive
* estimates of the solution will go to zero.
* This program carries out such an iteration, using a tolerance specified by
* the user, and writes the final estimate of the solution to a file that can
* be used for graphic processing.
* icensing:
* This code is distributed under the GNU LGPL license.
* odified:
* 18 October 2011
* uthor:
* Original C version by Michael Quinn.
* This C version by John Burkardt.
* eference:
* Michael Quinn,
* Parallel Programming in C with MPI and OpenMP,
* McGraw-Hill, 2004,
* ISBN13: 978-0071232654,
* LC: QA76.73.C15.Q55.
* ocal parameters:
* Local, double DIFF, the norm of the change in the solution from one iteration
* to the next.
* Local, double MEAN, the average of the boundary values, used to initialize
* the values of the solution in the interior.
* Local, double U[M][N], the solution at the previous iteration.
* Local, double W[M][N], the solution computed at the latest iteration.
*
*
* @see https://en.wikipedia.org/wiki/Jacobi_method
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include "utils.h"
static int N;
static int MAX_ITERATIONS;
static int SEED;
static double CONVERGENCE_THRESHOLD;
static FILE *data;
#define SEPARATOR "------------------------------------\n"
// Return the current time in seconds since the Epoch
double get_timestamp();
// Parse command line arguments to set solver parameters
void parse_arguments(int argc, char *argv[]);
// Run the Jacobi solver
// Returns the number of iterations performed
int run(double *restrict A, double *restrict xtmp)
{
int iter = 0, iterations_print = 1;
double err = 0.0;
#pragma omp target enter data map(to \
: A [0:N * N]) map(alloc \
: xtmp [0:N * N])
do
{
err = 0.0;
#pragma omp target teams num_teams(N / NTHREADS_GPU) thread_limit(NTHREADS_GPU) map(tofrom \
: err)
#pragma omp distribute parallel for collapse(2) num_threads(NTHREADS_GPU) dist_schedule(static, NTHREADS_GPU) reduction(max \
: err)
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
double diff = fabs(xtmp[i * N + j] - A[i * N + j]);
int swap = diff > err;
err = diff * swap + err * !swap;
}
}
#pragma omp target teams num_teams(N / NTHREADS_GPU) thread_limit(NTHREADS_GPU)
#pragma omp distribute parallel for collapse(2) num_threads(NTHREADS_GPU) dist_schedule(static, NTHREADS_GPU)
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A[i * N + j] = xtmp[i * N + j];
}
}
iter++;
#ifdef DEBUG
if (iter == iterations_print)
{
printf(" %8d %f\n", iter, err);
iterations_print = 2 * iterations_print;
}
#endif
} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
#pragma omp target exit data map(from \
: A [0:N * N]) map(release \
: xtmp)
return iter;
}
int main(int argc, char *argv[])
{
parse_arguments(argc, argv);
double *A = malloc(N * N * sizeof(double));
double *xtmp = malloc(N * N * sizeof(double));
printf(SEPARATOR);
printf("Matrix size: %dx%d\n", N, N);
printf("Maximum iterations: %d\n", MAX_ITERATIONS);
printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
printf(SEPARATOR);
for (int ii = 0; ii < N; ii++)
{
for (int jj = 0; jj < N; jj++)
{
double f;
fread(&f, sizeof(double), 1, data);
A[ii * N + jj] = f;
}
}
// Run Jacobi solver
start_timer();
int itr = run(A, xtmp);
stop_timer();
printf("Iterations = %d\n", itr);
printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
if (itr == MAX_ITERATIONS)
printf("WARNING: solution did not converge\n");
printf(SEPARATOR);
free(A);
free(xtmp);
fclose(data);
return 0;
}
int parse_int(const char *str)
{
char *next;
int value = strtoul(str, &next, 10);
return strlen(next) ? -1 : value;
}
double parse_double(const char *str)
{
char *next;
double value = strtod(str, &next);
return strlen(next) ? -1 : value;
}
void parse_arguments(int argc, char *argv[])
{
// Set default values
N = 500;
MAX_ITERATIONS = 2000;
CONVERGENCE_THRESHOLD = 0.001;
SEED = 0;
for (int i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
{
if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
{
printf("Invalid convergence threshold\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
{
if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
{
printf("Invalid number of iterations\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
{
if (++i >= argc || (N = parse_int(argv[i])) < 0)
{
printf("Invalid matrix order\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
{
printf("\n");
printf("Usage: ./jacobi [OPTIONS]\n\n");
printf("Options:\n");
printf(" -h --help Print this message\n");
printf(" -c --convergence C Set convergence threshold\n");
printf(" -i --iterations I Set maximum number of iterations\n");
printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
printf("\n");
exit(0);
}
else
{
printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
exit(1);
}
}
if (N == 1000)
data = fopen("data/jacobi-1000.bin", "rb");
else if (N == 500)
data = fopen("data/jacobi-500.bin", "rb");
else
{
printf("Invalid matrix order\n");
exit(1);
}
}

291
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@ -0,0 +1,291 @@
/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file jacobi.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief This code solves the steady state heat equation on a rectangular region.
* This code solves the steady state heat equation on a rectangular region.
* The sequential version of this program needs approximately
* 18/epsilon iterations to complete.
* The physical region, and the boundary conditions, are suggested
* by this diagram;
* W = 0
* +------------------+
* | |
* W = 100 | | W = 100
* | |
* +------------------+
* W = 100
* The region is covered with a grid of M by N nodes, and an N by N
* array W is used to record the temperature. The correspondence between
* array indices and locations in the region is suggested by giving the
* indices of the four corners:
* I = 0
* [0][0]-------------[0][N-1]
* | |
* J = 0 | | J = N-1
* | |
* [M-1][0]-----------[M-1][N-1]
* I = M-1
* The steady state solution to the discrete heat equation satisfies the
* following condition at an interior grid point:
* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* where "Central" is the index of the grid point, "North" is the index
* of its immediate neighbor to the "north", and so on.
*
* Given an approximate solution of the steady state heat equation, a
* "better" solution is given by replacing each interior point by the
* average of its 4 neighbors - in other words, by using the condition
* as an ASSIGNMENT statement:
* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* If this process is repeated often enough, the difference between successive
* estimates of the solution will go to zero.
* This program carries out such an iteration, using a tolerance specified by
* the user, and writes the final estimate of the solution to a file that can
* be used for graphic processing.
* icensing:
* This code is distributed under the GNU LGPL license.
* odified:
* 18 October 2011
* uthor:
* Original C version by Michael Quinn.
* This C version by John Burkardt.
* eference:
* Michael Quinn,
* Parallel Programming in C with MPI and OpenMP,
* McGraw-Hill, 2004,
* ISBN13: 978-0071232654,
* LC: QA76.73.C15.Q55.
* ocal parameters:
* Local, double DIFF, the norm of the change in the solution from one iteration
* to the next.
* Local, double MEAN, the average of the boundary values, used to initialize
* the values of the solution in the interior.
* Local, double U[M][N], the solution at the previous iteration.
* Local, double W[M][N], the solution computed at the latest iteration.
*
*
* @see https://en.wikipedia.org/wiki/Jacobi_method
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include "utils.h"
static int N;
static int MAX_ITERATIONS;
static int SEED;
static double CONVERGENCE_THRESHOLD;
static FILE *data;
#define SEPARATOR "------------------------------------\n"
// Return the current time in seconds since the Epoch
double get_timestamp();
// Parse command line arguments to set solver parameters
void parse_arguments(int argc, char *argv[]);
// Run the Jacobi solver
// Returns the number of iterations performed
int run(double *restrict A, double *restrict xtmp)
{
int iter = 0, iterations_print = 1;
double err = 0.0;
#pragma omp target enter data map(to \
: A [0:N * N]) map(alloc \
: xtmp [0:N * N])
do
{
err = 0.0;
#pragma omp target teams num_teams(N / NTHREADS_GPU) thread_limit(NTHREADS_GPU) map(tofrom \
: err)
#pragma omp distribute parallel for collapse(2) num_threads(NTHREADS_GPU) dist_schedule(static, NTHREADS_GPU) reduction(max \
: err)
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
err = fmax(err, fabs(xtmp[i * N + j] - A[i * N + j]));
}
}
//#pragma omp target update from(xtmp[0:N*N])
#pragma omp target teams num_teams(N / NTHREADS_GPU) thread_limit(NTHREADS_GPU)
#pragma omp distribute parallel for collapse(2) num_threads(NTHREADS_GPU) dist_schedule(static, NTHREADS_GPU)
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A[i * N + j] = xtmp[i * N + j];
}
}
iter++;
#ifdef DEBUG
if (iter == iterations_print)
{
printf(" %8d %f\n", iter, err);
iterations_print = 2 * iterations_print;
}
#endif
} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
#pragma omp target exit data map(from \
: A [0:N * N]) map(release \
: xtmp)
return iter;
}
int main(int argc, char *argv[])
{
parse_arguments(argc, argv);
double *A = malloc(N * N * sizeof(double));
double *xtmp = malloc(N * N * sizeof(double));
printf(SEPARATOR);
printf("Matrix size: %dx%d\n", N, N);
printf("Maximum iterations: %d\n", MAX_ITERATIONS);
printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
printf(SEPARATOR);
for (int ii = 0; ii < N; ii++)
{
for (int jj = 0; jj < N; jj++)
{
double f;
fread(&f, sizeof(double), 1, data);
A[ii * N + jj] = f;
}
}
// Run Jacobi solver
start_timer();
int itr = run(A, xtmp);
stop_timer();
printf("Iterations = %d\n", itr);
printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
if (itr == MAX_ITERATIONS)
printf("WARNING: solution did not converge\n");
printf(SEPARATOR);
free(A);
free(xtmp);
fclose(data);
return 0;
}
int parse_int(const char *str)
{
char *next;
int value = strtoul(str, &next, 10);
return strlen(next) ? -1 : value;
}
double parse_double(const char *str)
{
char *next;
double value = strtod(str, &next);
return strlen(next) ? -1 : value;
}
void parse_arguments(int argc, char *argv[])
{
// Set default values
N = 500;
MAX_ITERATIONS = 2000;
CONVERGENCE_THRESHOLD = 0.001;
SEED = 0;
for (int i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
{
if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
{
printf("Invalid convergence threshold\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
{
if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
{
printf("Invalid number of iterations\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
{
if (++i >= argc || (N = parse_int(argv[i])) < 0)
{
printf("Invalid matrix order\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
{
printf("\n");
printf("Usage: ./jacobi [OPTIONS]\n\n");
printf("Options:\n");
printf(" -h --help Print this message\n");
printf(" -c --convergence C Set convergence threshold\n");
printf(" -i --iterations I Set maximum number of iterations\n");
printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
printf("\n");
exit(0);
}
else
{
printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
exit(1);
}
}
if (N == 1000)
data = fopen("data/jacobi-1000.bin", "rb");
else if (N == 500)
data = fopen("data/jacobi-500.bin", "rb");
else
{
printf("Invalid matrix order\n");
exit(1);
}
}

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#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include "utils.h"
#ifndef N
#define N (1 << 11)
#endif
#pragma omp declare target
#define SM 64
static void reorder2(float *restrict a, float *restrict b, int n)
{
for (int i = 0; i < SM; i++)
for (int j = 0; j < SM; j++)
b[i * SM + j] = a[i * n + j];
}
static void kernel(float *restrict a, float *restrict b, float *restrict c, int n)
{
for (int i = 0; i < SM; i++)
{
for (int k = 0; k < SM; k++)
{
for (int j = 0; j < SM; j++)
{
c[i * n + j] += a[i * n + k] * b[k * SM + j];
}
}
}
}
void gemm_acc(float *restrict a, float *restrict b, float *restrict c, int n)
{
int bk = n / SM;
#pragma omp target data map(to \
: n, bk, a [0:n * n], b [0:n * n]) map(from \
: c[:n * n])
#pragma omp target teams num_teams(bk / NTHREADS_GPU) thread_limit(NTHREADS_GPU) map(to \
: n, bk, a [0:n * n], b [0:n * n]) map(from \
: c[:n * n])
#pragma omp distribute parallel for num_threads(NTHREADS_GPU) collapse(3) dist_schedule(static, NTHREADS_GPU)
for (int i = 0; i < bk; i++)
{
for (int j = 0; j < bk; j++)
{
for (int k = 0; k < bk; k++)
{
float b2[SM * SM];
reorder2(&b[SM * (k * n + j)], b2, n);
kernel(&a[SM * (i * n + k)], b2, &c[SM * (i * n + j)], n);
}
}
}
}
#pragma omp end declare target
void gemm_opt(float *restrict a, float *restrict b, float *restrict c, int n)
{
int bk = n / SM;
float b2[SM * SM];
for (int i = 0; i < bk; i++)
{
for (int j = 0; j < bk; j++)
{
for (int k = 0; k < bk; k++)
{
reorder2(&b[SM * (k * n + j)], b2, n);
kernel(&a[SM * (i * n + k)], b2, &c[SM * (i * n + j)], n);
}
}
}
}
void gemm(float *restrict a, float *restrict b, float *restrict c, int n)
{
int i, j, k;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
float sum = 0.0;
for (int k = 0; k < n; ++k)
{
sum += a[i + k * n] * b[k + j * n];
}
c[i * n + j] += sum;
}
}
}
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float *a, *b, *c, *g;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (a = (float *)malloc(sizeof(*a) * n * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (b = (float *)malloc(sizeof(*b) * n * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (c = (float *)malloc(sizeof(*c) * n * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (NULL == (g = (float *)malloc(sizeof(*g) * n * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(a);
free(b);
free(c);
free(g);
exit(EXIT_FAILURE);
}
if (n <= 1024)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
}
if (n <= 4096)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_opt(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm_opt on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
}
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_acc(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm_acc : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
if (n <= 4096)
for (i = 0; i < n; i++)
{
iret = *(int *)(g + i) ^ *(int *)(c + i);
assert(iret == 0);
}
return 0;
}

500
openmp/lab3/.solutions/matmul-omp2.c Normal file
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#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include <cuda_runtime.h>
#include "cublas_v2.h"
#ifndef N
#define N (1 << 10)
#endif
#pragma omp declare target
#define SM 64
#define NTHRDS7 (1 << 0x7) /* 2^{7} */
#define NTHRDS8 (1 << 0x8) /* 2^{8} */
#define NTHRDS9 (1 << 0x9) /* 2^{9} */
#define LTEAMSD (1 << 0xD) /* 2^{13} */
#define LTEAMSE (1 << 0xE) /* 2^{14} */
#define LTEAMSF (1 << 0xF) /* 2^{15} */
#define LTEAMSG (1 << 020) /* 2^{16} */
#define BLKROW (512) /* 4x number of threads in each team */
#define BLKDIM (16)
void gemm_accel_opt2(float *restrict a, float *restrict b, float *restrict c, int n)
{
/*
* - jik-loop
* - 2^7 threads per team and 2^13 teams
* - collapse(3)
* - 4x j-loop unrolling (stride of 1 col )
* - 4x i-loop unrolling (stride of 2^7 rows)
* - 4x k-loop unrolling
* - rb: 4x data re-use
* - ra: 4x data re-use
* - register blocking
*/
#pragma omp target data \
map(to \
: n, a [0:n * n], b [0:n * n]) map(tofrom \
: c [0:n * n])
{
#pragma omp target teams num_teams(LTEAMSD) thread_limit(NTHRDS7) \
map(to \
: n, a [0:n * n], b [0:n * n]) map(tofrom \
: c [0:n * n]) default(none) shared(a, b, c, n)
#pragma omp distribute parallel for num_threads(NTHRDS7) \
dist_schedule(static, NTHRDS7) collapse(3) default(none) shared(a, b, c, n)
for (int j = 0; j < n; j += 4)
{ /* 4x unrolling */
for (int iblk = 0; iblk < n / BLKROW; ++iblk)
{
for (int i = 0; i < NTHRDS7; ++i)
{ /* 4x unrolling */
/* register for c: 4x j-loop * 4x i-loop */
float rc0, rc1, rc2, rc3,
rc4, rc5, rc6, rc7,
rc8, rc9, rca, rcb,
rcc, rcd, rce, rcf;
rc0 = c[j * n + iblk * BLKROW + i];
rc1 = c[j * n + iblk * BLKROW + i + NTHRDS7];
rc2 = c[j * n + iblk * BLKROW + i + NTHRDS7 * 2];
rc3 = c[j * n + iblk * BLKROW + i + NTHRDS7 * 3];
rc4 = c[(j + 1) * n + iblk * BLKROW + i];
rc5 = c[(j + 1) * n + iblk * BLKROW + i + NTHRDS7];
rc6 = c[(j + 1) * n + iblk * BLKROW + i + NTHRDS7 * 2];
rc7 = c[(j + 1) * n + iblk * BLKROW + i + NTHRDS7 * 3];
rc8 = c[(j + 2) * n + iblk * BLKROW + i];
rc9 = c[(j + 2) * n + iblk * BLKROW + i + NTHRDS7];
rca = c[(j + 2) * n + iblk * BLKROW + i + NTHRDS7 * 2];
rcb = c[(j + 2) * n + iblk * BLKROW + i + NTHRDS7 * 3];
rcc = c[(j + 3) * n + iblk * BLKROW + i];
rcd = c[(j + 3) * n + iblk * BLKROW + i + NTHRDS7];
rce = c[(j + 3) * n + iblk * BLKROW + i + NTHRDS7 * 2];
rcf = c[(j + 3) * n + iblk * BLKROW + i + NTHRDS7 * 3];
for (int k = 0; k < n; k += 4)
{ /* 4x unrolling */
/* register for b: 4x j-loop * 4x k-loop */
float rb0, rb1, rb2, rb3,
rb4, rb5, rb6, rb7,
rb8, rb9, rba, rbb,
rbc, rbd, rbe, rbf;
rb0 = b[j * n + k];
rb1 = b[j * n + k + 1];
rb2 = b[j * n + k + 2];
rb3 = b[j * n + k + 3];
rb4 = b[(j + 1) * n + k];
rb5 = b[(j + 1) * n + k + 1];
rb6 = b[(j + 1) * n + k + 2];
rb7 = b[(j + 1) * n + k + 3];
rb8 = b[(j + 2) * n + k];
rb9 = b[(j + 2) * n + k + 1];
rba = b[(j + 2) * n + k + 2];
rbb = b[(j + 2) * n + k + 3];
rbc = b[(j + 3) * n + k];
rbd = b[(j + 3) * n + k + 1];
rbe = b[(j + 3) * n + k + 2];
rbf = b[(j + 3) * n + k + 3];
/* register for a: 4x i-loop * 4x k-loop */
float ra0, ra1, ra2, ra3,
ra4, ra5, ra6, ra7,
ra8, ra9, raa, rab,
rac, rad, rae, raf;
ra0 = a[k * n + iblk * BLKROW + i];
ra1 = a[k * n + iblk * BLKROW + i + NTHRDS7];
ra2 = a[k * n + iblk * BLKROW + i + NTHRDS7 * 2];
ra3 = a[k * n + iblk * BLKROW + i + NTHRDS7 * 3];
ra4 = a[(k + 1) * n + iblk * BLKROW + i];
ra5 = a[(k + 1) * n + iblk * BLKROW + i + NTHRDS7];
ra6 = a[(k + 1) * n + iblk * BLKROW + i + NTHRDS7 * 2];
ra7 = a[(k + 1) * n + iblk * BLKROW + i + NTHRDS7 * 3];
ra8 = a[(k + 2) * n + iblk * BLKROW + i];
ra9 = a[(k + 2) * n + iblk * BLKROW + i + NTHRDS7];
raa = a[(k + 2) * n + iblk * BLKROW + i + NTHRDS7 * 2];
rab = a[(k + 2) * n + iblk * BLKROW + i + NTHRDS7 * 3];
rac = a[(k + 3) * n + iblk * BLKROW + i];
rad = a[(k + 3) * n + iblk * BLKROW + i + NTHRDS7];
rae = a[(k + 3) * n + iblk * BLKROW + i + NTHRDS7 * 2];
raf = a[(k + 3) * n + iblk * BLKROW + i + NTHRDS7 * 3];
/*
* register blocking
*/
// col 1 of c:
rc0 += ra0 * rb0;
rc0 += ra4 * rb1;
rc0 += ra8 * rb2;
rc0 += rac * rb3;
rc1 += ra1 * rb0;
rc1 += ra5 * rb1;
rc1 += ra9 * rb2;
rc1 += rad * rb3;
rc2 += ra2 * rb0;
rc2 += ra6 * rb1;
rc2 += raa * rb2;
rc2 += rae * rb3;
rc3 += ra3 * rb0;
rc3 += ra7 * rb1;
rc3 += rab * rb2;
rc3 += raf * rb3;
// col 2 of c:
rc4 += ra0 * rb4;
rc4 += ra4 * rb5;
rc4 += ra8 * rb6;
rc4 += rac * rb7;
rc5 += ra1 * rb4;
rc5 += ra5 * rb5;
rc5 += ra9 * rb6;
rc5 += rad * rb7;
rc6 += ra2 * rb4;
rc6 += ra6 * rb5;
rc6 += raa * rb6;
rc6 += rae * rb7;
rc7 += ra3 * rb4;
rc7 += ra7 * rb5;
rc7 += rab * rb6;
rc7 += raf * rb7;
// col 3 of c:
rc8 += ra0 * rb8;
rc8 += ra4 * rb9;
rc8 += ra8 * rba;
rc8 += rac * rbb;
rc9 += ra1 * rb8;
rc9 += ra5 * rb9;
rc9 += ra9 * rba;
rc9 += rad * rbb;
rca += ra2 * rb8;
rca += ra6 * rb9;
rca += raa * rba;
rca += rae * rbb;
rcb += ra3 * rb8;
rcb += ra7 * rb9;
rcb += rab * rba;
rcb += raf * rbb;
// col 4 of c:
rcc += ra0 * rbc;
rcc += ra4 * rbd;
rcc += ra8 * rbe;
rcc += rac * rbf;
rcd += ra1 * rbc;
rcd += ra5 * rbd;
rcd += ra9 * rbe;
rcd += rad * rbf;
rce += ra2 * rbc;
rce += ra6 * rbd;
rce += raa * rbe;
rce += rae * rbf;
rcf += ra3 * rbc;
rcf += ra7 * rbd;
rcf += rab * rbe;
rcf += raf * rbf;
}
c[j * n + iblk * BLKROW + i] = rc0;
c[j * n + iblk * BLKROW + i + NTHRDS7] = rc1;
c[j * n + iblk * BLKROW + i + NTHRDS7 * 2] = rc2;
c[j * n + iblk * BLKROW + i + NTHRDS7 * 3] = rc3;
c[(j + 1) * n + iblk * BLKROW + i] = rc4;
c[(j + 1) * n + iblk * BLKROW + i + NTHRDS7] = rc5;
c[(j + 1) * n + iblk * BLKROW + i + NTHRDS7 * 2] = rc6;
c[(j + 1) * n + iblk * BLKROW + i + NTHRDS7 * 3] = rc7;
c[(j + 2) * n + iblk * BLKROW + i] = rc8;
c[(j + 2) * n + iblk * BLKROW + i + NTHRDS7] = rc9;
c[(j + 2) * n + iblk * BLKROW + i + NTHRDS7 * 2] = rca;
c[(j + 2) * n + iblk * BLKROW + i + NTHRDS7 * 3] = rcb;
c[(j + 3) * n + iblk * BLKROW + i] = rcc;
c[(j + 3) * n + iblk * BLKROW + i + NTHRDS7] = rcd;
c[(j + 3) * n + iblk * BLKROW + i + NTHRDS7 * 2] = rce;
c[(j + 3) * n + iblk * BLKROW + i + NTHRDS7 * 3] = rcf;
} /* end i-loop */
} /* end iblk-loop */
} /* end j-loop */
}
}
void gemm_cublas(float *restrict a, float *restrict b, float *restrict c, int n)
{
cublasHandle_t handle;
float alfa = 1.0f,
beta = 1.0f,
*a_dev = NULL,
*b_dev = NULL,
*c_dev = NULL;
/*
* cublasSgemm in CUBLAS
*/
if (CUBLAS_STATUS_SUCCESS != cublasCreate(&handle))
{
printf("error: initialization (CUBLAS)\n");
cublasDestroy(handle);
exit(EXIT_FAILURE);
}
if (cudaSuccess != cudaMalloc((void **)&a_dev, sizeof(*a) * n * n) ||
cudaSuccess != cudaMalloc((void **)&b_dev, sizeof(*b) * n * n) ||
cudaSuccess != cudaMalloc((void **)&c_dev, sizeof(*c) * n * n))
{
printf("error: memory allocation (CUDA)\n");
cudaFree(a_dev);
cudaFree(b_dev);
cudaFree(c_dev);
cublasDestroy(handle);
exit(EXIT_FAILURE);
}
if (CUBLAS_STATUS_SUCCESS != cublasSetMatrix(n, n, sizeof(*a), a, n, a_dev, n) ||
CUBLAS_STATUS_SUCCESS != cublasSetMatrix(n, n, sizeof(*b), b, n, b_dev, n) ||
CUBLAS_STATUS_SUCCESS != cublasSetMatrix(n, n, sizeof(*c), c, n, c_dev, n))
{
printf("error: host --> accl (CUBLAS)\n");
cudaFree(a_dev);
cudaFree(b_dev);
cudaFree(c_dev);
cublasDestroy(handle);
exit(EXIT_FAILURE);
}
if (CUBLAS_STATUS_SUCCESS != cublasSgemm(handle, CUBLAS_OP_N, CUBLAS_OP_N,
n, n, n, &alfa, a_dev, n, b_dev, n, &beta, c_dev, n))
{
printf("error: cublasSgemm (CUBLAS)\n");
cudaFree(a_dev);
cudaFree(b_dev);
cudaFree(c_dev);
cublasDestroy(handle);
exit(EXIT_FAILURE);
}
if (cudaSuccess != cudaDeviceSynchronize())
{
printf("error: device synchronization (CUDA)\n");
cudaFree(a_dev);
cudaFree(b_dev);
cudaFree(c_dev);
cublasDestroy(handle);
exit(EXIT_FAILURE);
}
if (CUBLAS_STATUS_SUCCESS != cublasGetMatrix(n, n, sizeof(*c), c_dev, n, c, n))
{
printf("error: accl --> host (CUBLAS)\n");
cudaFree(a_dev);
cudaFree(b_dev);
cudaFree(c_dev);
cublasDestroy(handle);
exit(EXIT_FAILURE);
}
cudaFree(a_dev);
cudaFree(b_dev);
cudaFree(c_dev);
cublasDestroy(handle);
}
static void reorder2(float *restrict a, float *restrict b, int n)
{
for (int i = 0; i < SM; i++)
for (int j = 0; j < SM; j++)
b[i * SM + j] = a[i * n + j];
}
static void kernel(float *restrict a, float *restrict b, float *restrict c, int n)
{
for (int i = 0; i < SM; i++)
{
for (int k = 0; k < SM; k++)
{
for (int j = 0; j < SM; j++)
{
c[i * n + j] += a[i * n + k] * b[k * SM + j];
}
}
}
}
void gemm_accel_opt(float *restrict a, float *restrict b, float *restrict c, int n)
{
#pragma omp target teams distribute parallel for collapse(3) map(to \
: n, a [0:n * n], b [0:n * n]) map(from \
: c [0:n * n]) schedule(static, 1)
for (int i = 0; i < n / SM; i++)
{
for (int j = 0; j < n / SM; j++)
{
for (int k = 0; k < n / SM; k++)
{
float b2[SM * SM];
reorder2(&b[SM * (k * n + j)], b2, n);
kernel(&a[SM * (i * n + k)], b2, &c[SM * (i * n + j)], n);
}
}
}
}
#pragma omp end declare target
void gemm_opt(float *restrict a, float *restrict b, float *restrict c, int n)
{
int bk = n / SM;
#pragma omp parallel
{
float b2[SM * SM];
#pragma omp for collapse(3)
for (int i = 0; i < bk; i++)
{
for (int j = 0; j < bk; j++)
{
for (int k = 0; k < bk; k++)
{
reorder2(&b[SM * (k * n + j)], b2, n);
kernel(&a[SM * (i * n + k)], b2, &c[SM * (i * n + j)], n);
}
}
}
}
}
void gemm(float *restrict a, float *restrict b, float *restrict c, int n)
{
int i, j, k;
#pragma omp parallel for simd collapse(2) schedule(simd \
: static)
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
float sum = 0.0;
for (int k = 0; k < n; ++k)
{
sum += a[i + k * n] * b[k + j * n];
}
c[i * n + j] += sum;
}
}
}
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float *a, *b, *c, *g;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (a = (float *)malloc(sizeof(*a) * n * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (b = (float *)malloc(sizeof(*b) * n * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (c = (float *)malloc(sizeof(*c) * n * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (NULL == (g = (float *)malloc(sizeof(*g) * n * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(a);
free(b);
free(c);
free(g);
exit(EXIT_FAILURE);
}
if (n <= 1024)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
}
if (n <= 4096)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_opt(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm_opt on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
}
#if 0
#pragma omp target teams distribute parallel for map(to \
: a [0:n * n], b [0:n * n]) map(from \
: c [0:n * n]) collapse(2)
for(int i = 0; i < n; ++i){
for(int j = 0; j < n; ++j){
float sum = 0.0;
for(int k = 0; k < n; ++k){
sum += a[i+k*n]*b[k+j*n];
}
c[i*n+j] += sum;
}
}
#endif
if (n <= 4096)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_accel_opt(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("GEMM-opt1 on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
for (i = 0; i < n; i++)
{
iret = *(int *)(g + i) ^ *(int *)(c + i);
assert(iret == 0);
}
}
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_accel_opt2(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("GEMM-opt2 on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
if (n <= 4096)
for (i = 0; i < n; i++)
{
iret = *(int *)(g + i) ^ *(int *)(c + i);
assert(iret == 0);
}
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_cublas(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("CUBLAS on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
if (n <= 4096)
for (i = 0; i < n; i++)
{
iret = *(int *)(g + i) ^ *(int *)(c + i);
assert(iret == 0);
}
free(a);
free(b);
free(c);
free(g);
return 0;
}

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openmp/lab3/.solutions/saxpy-omp1.c Normal file
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/**
* @file saxpy.c
*
* @brief saxpy performs the \c axpy computation in single-precision on both
* host and accelerator. The performance (in MFLOPS) on host and accelerator is
* compared and the numerical results are also verified for consistency.
*
* The \c axpy computation is defined as:
*
* y := a * x + y
*
* where:
*
* - a is a scalar.
* - x and y are vectors each with n elements.
*
* Please note that in this version only <em>one GPU thread</em> is used.
*
* Offload to GPU:
*
* gcc -fopenmp -foffload=nvptx-none saxpy.c
*
*/
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include "utils.h"
#define TWO02 (1 << 2)
#define TWO04 (1 << 4)
#define TWO08 (1 << 8)
#ifndef N
#define N (1 << 20)
#endif
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float a = 101.0f / TWO02,
b, c,
*x, *y, *z;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (x = (float *)malloc(sizeof(*x) * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (y = (float *)malloc(sizeof(*y) * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (z = (float *)malloc(sizeof(*z) * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(x);
free(y);
free(z);
exit(EXIT_FAILURE);
}
b = rand() % TWO04;
c = rand() % TWO08;
for (i = 0; i < n; i++)
{
x[i] = b / (float)TWO02;
y[i] = z[i] = c / (float)TWO04;
}
/*
* 1. saxpy on host
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
for (i = 0; i < n; i++)
{
y[i] = a * x[i] + y[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 2. saxpy on accel
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
#pragma omp target map(to \
: a, n, x [0:n]) map(tofrom \
: z [0:n])
for (int i = 0; i < n; i++)
{
z[i] = a * x[i] + z[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 3. verify numerical consistency
*/
for (i = 0; i < n; i++)
{
iret = *(int *)(y + i) ^ *(int *)(z + i);
assert(iret == 0);
}
return 0;
}

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/**
* @file saxpy.c
*
* @brief saxpy performs the \c axpy computation in single-precision on both
* host and accelerator. The performance (in MFLOPS) on host and accelerator is
* compared and the numerical results are also verified for consistency.
*
* The \c axpy computation is defined as:
*
* y := a * x + y
*
* where:
*
* - a is a scalar.
* - x and y are vectors each with n elements.
*
* Please note that in this version only <em>one GPU thread</em> is used.
*
* Offload to GPU:
*
* gcc -fopenmp -foffload=nvptx-none saxpy.c
*
*/
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include "utils.h"
#define TWO02 (1 << 2)
#define TWO04 (1 << 4)
#define TWO08 (1 << 8)
#ifndef N
#define N (1 << 20)
#endif
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float a = 101.0f / TWO02,
b, c,
*x, *y, *z;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (x = (float *)malloc(sizeof(*x) * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (y = (float *)malloc(sizeof(*y) * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (z = (float *)malloc(sizeof(*z) * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(x);
free(y);
free(z);
exit(EXIT_FAILURE);
}
b = rand() % TWO04;
c = rand() % TWO08;
for (i = 0; i < n; i++)
{
x[i] = b / (float)TWO02;
y[i] = z[i] = c / (float)TWO04;
}
/*
* 1. saxpy on host
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
for (i = 0; i < n; i++)
{
y[i] = a * x[i] + y[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 2. saxpy on accel
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
#pragma omp target parallel for map(to \
: a, n, x [0:n]) map(tofrom \
: z [0:n])
for (int i = 0; i < n; i++)
{
z[i] = a * x[i] + z[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 3. verify numerical consistency
*/
for (i = 0; i < n; i++)
{
iret = *(int *)(y + i) ^ *(int *)(z + i);
assert(iret == 0);
}
return 0;
}

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/**
* @file saxpy.c
*
* @brief saxpy performs the \c axpy computation in single-precision on both
* host and accelerator. The performance (in MFLOPS) on host and accelerator is
* compared and the numerical results are also verified for consistency.
*
* The \c axpy computation is defined as:
*
* y := a * x + y
*
* where:
*
* - a is a scalar.
* - x and y are vectors each with n elements.
*
* Please note that in this version only <em>one GPU thread</em> is used.
*
* Offload to GPU:
*
* gcc -fopenmp -foffload=nvptx-none saxpy.c
*
*/
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include "utils.h"
#define TWO02 (1 << 2)
#define TWO04 (1 << 4)
#define TWO08 (1 << 8)
#ifndef N
#define N (1 << 27)
#endif
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float a = 101.0f / TWO02,
b, c,
*x, *y, *z;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (x = (float *)malloc(sizeof(*x) * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (y = (float *)malloc(sizeof(*y) * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (z = (float *)malloc(sizeof(*z) * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(x);
free(y);
free(z);
exit(EXIT_FAILURE);
}
b = rand() % TWO04;
c = rand() % TWO08;
for (i = 0; i < n; i++)
{
x[i] = b / (float)TWO02;
y[i] = z[i] = c / (float)TWO04;
}
/*
* 1. saxpy on host
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
for (i = 0; i < n; i++)
{
y[i] = a * x[i] + y[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 2. saxpy on accel
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
#pragma omp target data map(to \
: a, n, x [0:n]) map(tofrom \
: z [0:n])
#pragma omp target teams num_teams(n / NTHREADS_GPU) thread_limit(NTHREADS_GPU) \
map(to \
: a, n, x [0:n]) map(tofrom \
: z [0:n])
#pragma omp distribute parallel for num_threads(NTHREADS_GPU) \
dist_schedule(static, NTHREADS_GPU)
for (int i = 0; i < n; i++)
{
z[i] = a * x[i] + z[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 3. verify numerical consistency
*/
for (i = 0; i < n; i++)
{
iret = *(int *)(y + i) ^ *(int *)(z + i);
assert(iret == 0);
}
return 0;
}

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/**
* @file saxpy.c
*
* @brief saxpy performs the \c axpy computation in single-precision on both
* host and accelerator. The performance (in MFLOPS) on host and accelerator is
* compared and the numerical results are also verified for consistency.
*
* The \c axpy computation is defined as:
*
* y := a * x + y
*
* where:
*
* - a is a scalar.
* - x and y are vectors each with n elements.
*
* Please note that in this version only <em>one GPU thread</em> is used.
*
* Offload to GPU:
*
* gcc -fopenmp -foffload=nvptx-none saxpy.c
*
*/
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include "utils.h"
#define TWO02 (1 << 2)
#define TWO04 (1 << 4)
#define TWO08 (1 << 8)
#ifndef N
#define N (1 << 27)
#endif
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float a = 101.0f / TWO02,
b, c,
*x, *y, *z;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (x = (float *)malloc(sizeof(*x) * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (y = (float *)malloc(sizeof(*y) * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (z = (float *)malloc(sizeof(*z) * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(x);
free(y);
free(z);
exit(EXIT_FAILURE);
}
b = rand() % TWO04;
c = rand() % TWO08;
for (i = 0; i < n; i++)
{
x[i] = b / (float)TWO02;
y[i] = z[i] = c / (float)TWO04;
}
/*
* 1. saxpy on host
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
for (i = 0; i < n; i++)
{
y[i] = a * x[i] + y[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 2. saxpy on accel
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
int BLOCK=n/8;
for (int i = 0; i < n; i+=BLOCK)
{
#pragma omp target teams distribute parallel for map(to: a, x [i:BLOCK]) map(tofrom: z [i:BLOCK]) nowait
for (int ii = 0; ii < BLOCK; ii++)
{
z[i+ii] = a * x[i+ii] + z[i+ii];
}
}
#pragma omp taskwait
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 3. verify numerical consistency
*/
for (i = 0; i < n; i++)
{
iret = *(int *)(y + i) ^ *(int *)(z + i);
assert(iret == 0);
}
return 0;
}

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ifndef EXERCISE
EXERCISE=exercise1.c
endif
CC=clang
LD=ld
OBJDUMP=objdump
OPT=-O3 -g
OMP=-fopenmp=libomp -fopenmp-targets=nvptx64-nvidia-cuda
CFLAGS=$(OPT) $(OMP) -I. $(EXT_CFLAGS)
LDFLAGS=-lm $(EXT_LDFLAGS)
SRCS=utils.c
OBJS=$(SRCS:.c=.o) $(EXERCISE:.c=.o)
EXE=$(EXERCISE:.c=.exe)
$(EXE): $(OBJS)
$(CC) $(CFLAGS) $(OBJS) -o $@ $(LDFLAGS)
all: $(EXE)
.PHONY: run profile clean
run: $(EXE)
./$(EXE)
profile: $(EXE)
sudo LD_LIBRARY_PATH=/usr/local/cuda/lib:/usr/ext/lib:${LD_LIBRARY_PATH} LIBRARY_PATH=/usr/ext/lib:${LIBRARY_PATH} nvprof ./$(EXE)
clean:
rm -f $(OBJS) *.o *.exe *.out *~

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openmp/lab3/jacobi.c Normal file
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/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file jacobi.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief This code solves the steady state heat equation on a rectangular region.
* This code solves the steady state heat equation on a rectangular region.
* The sequential version of this program needs approximately
* 18/epsilon iterations to complete.
* The physical region, and the boundary conditions, are suggested
* by this diagram;
* W = 0
* +------------------+
* | |
* W = 100 | | W = 100
* | |
* +------------------+
* W = 100
* The region is covered with a grid of M by N nodes, and an N by N
* array W is used to record the temperature. The correspondence between
* array indices and locations in the region is suggested by giving the
* indices of the four corners:
* I = 0
* [0][0]-------------[0][N-1]
* | |
* J = 0 | | J = N-1
* | |
* [M-1][0]-----------[M-1][N-1]
* I = M-1
* The steady state solution to the discrete heat equation satisfies the
* following condition at an interior grid point:
* W[Central] = (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* where "Central" is the index of the grid point, "North" is the index
* of its immediate neighbor to the "north", and so on.
*
* Given an approximate solution of the steady state heat equation, a
* "better" solution is given by replacing each interior point by the
* average of its 4 neighbors - in other words, by using the condition
* as an ASSIGNMENT statement:
* W[Central] <= (1/4) * ( W[North] + W[South] + W[East] + W[West] )
* If this process is repeated often enough, the difference between successive
* estimates of the solution will go to zero.
* This program carries out such an iteration, using a tolerance specified by
* the user, and writes the final estimate of the solution to a file that can
* be used for graphic processing.
* icensing:
* This code is distributed under the GNU LGPL license.
* odified:
* 18 October 2011
* uthor:
* Original C version by Michael Quinn.
* This C version by John Burkardt.
* eference:
* Michael Quinn,
* Parallel Programming in C with MPI and OpenMP,
* McGraw-Hill, 2004,
* ISBN13: 978-0071232654,
* LC: QA76.73.C15.Q55.
* ocal parameters:
* Local, double DIFF, the norm of the change in the solution from one iteration
* to the next.
* Local, double MEAN, the average of the boundary values, used to initialize
* the values of the solution in the interior.
* Local, double U[M][N], the solution at the previous iteration.
* Local, double W[M][N], the solution computed at the latest iteration.
*
*
* @see https://en.wikipedia.org/wiki/Jacobi_method
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
#include <sys/time.h>
#include "utils.h"
static int N;
static int MAX_ITERATIONS;
static int SEED;
static double CONVERGENCE_THRESHOLD;
static FILE *data;
#define SEPARATOR "------------------------------------\n"
// Return the current time in seconds since the Epoch
double get_timestamp();
// Parse command line arguments to set solver parameters
void parse_arguments(int argc, char *argv[]);
// Run the Jacobi solver
// Returns the number of iterations performed
int run(double *A, double *xtmp)
{
int iter = 0, iterations_print = 1;
double err = 0.0;
do
{
err = 0.0;
#pragma omp parallel for reduction(max \
: err) num_threads(NTHREADS)
for (int i = 1; i < N - 1; i++)
{
for (int j = 1; j < N - 1; j++)
{
xtmp[i * N + j] = 0.25 * (A[(i - 1) * N + j] + A[(i + 1) * N + j] + A[i * N + j - 1] + A[i * N + j + 1]);
err = fmax(err, fabs(xtmp[i * N + j] - A[i * N + j]));
}
}
#pragma omp parallel for num_threads(NTHREADS)
for (int i = 0; i < N; i++)
{
for (int j = 0; j < N; j++)
{
A[i * N + j] = xtmp[i * N + j];
}
}
iter++;
#ifdef DEBUG
if (iter == iterations_print)
{
printf(" %8d %f\n", iter, err);
iterations_print = 2 * iterations_print;
}
#endif
} while (err > CONVERGENCE_THRESHOLD && iter < MAX_ITERATIONS);
return iter;
}
int main(int argc, char *argv[])
{
parse_arguments(argc, argv);
double *A = malloc(N * N * sizeof(double));
double *xtmp = malloc(N * N * sizeof(double));
printf(SEPARATOR);
printf("Matrix size: %dx%d\n", N, N);
printf("Maximum iterations: %d\n", MAX_ITERATIONS);
printf("Convergence threshold: %lf\n", CONVERGENCE_THRESHOLD);
printf(SEPARATOR);
for (int ii = 0; ii < N; ii++)
{
for (int jj = 0; jj < N; jj++)
{
double f;
fread(&f, sizeof(double), 1, data);
A[ii * N + jj] = f;
}
}
// Run Jacobi solver
start_timer();
int itr = run(A, xtmp);
stop_timer();
printf("Iterations = %d\n", itr);
printf("Solver runtime = %lf ms\n", elapsed_ns() / 1E6);
if (itr == MAX_ITERATIONS)
printf("WARNING: solution did not converge\n");
printf(SEPARATOR);
free(A);
free(xtmp);
fclose(data);
return 0;
}
int parse_int(const char *str)
{
char *next;
int value = strtoul(str, &next, 10);
return strlen(next) ? -1 : value;
}
double parse_double(const char *str)
{
char *next;
double value = strtod(str, &next);
return strlen(next) ? -1 : value;
}
void parse_arguments(int argc, char *argv[])
{
// Set default values
N = 500;
MAX_ITERATIONS = 2000;
CONVERGENCE_THRESHOLD = 0.001;
SEED = 0;
for (int i = 1; i < argc; i++)
{
if (!strcmp(argv[i], "--convergence") || !strcmp(argv[i], "-c"))
{
if (++i >= argc || (CONVERGENCE_THRESHOLD = parse_double(argv[i])) < 0)
{
printf("Invalid convergence threshold\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--iterations") || !strcmp(argv[i], "-i"))
{
if (++i >= argc || (MAX_ITERATIONS = parse_int(argv[i])) < 0)
{
printf("Invalid number of iterations\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--norder") || !strcmp(argv[i], "-n"))
{
if (++i >= argc || (N = parse_int(argv[i])) < 0)
{
printf("Invalid matrix order\n");
exit(1);
}
}
else if (!strcmp(argv[i], "--help") || !strcmp(argv[i], "-h"))
{
printf("\n");
printf("Usage: ./jacobi [OPTIONS]\n\n");
printf("Options:\n");
printf(" -h --help Print this message\n");
printf(" -c --convergence C Set convergence threshold\n");
printf(" -i --iterations I Set maximum number of iterations\n");
printf(" -n --norder N Set maxtrix order (500 or 1000)\n");
printf("\n");
exit(0);
}
else
{
printf("Unrecognized argument '%s' (try '--help')\n", argv[i]);
exit(1);
}
}
if (N == 1000)
data = fopen("data/jacobi-1000.bin", "rb");
else if (N == 500)
data = fopen("data/jacobi-500.bin", "rb");
else
{
printf("Invalid matrix order\n");
exit(1);
}
}

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#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#ifndef N
#define N (1 << 10)
#endif
#pragma omp declare target
#define SM 64
static void reorder2(float *restrict a, float *restrict b, int n)
{
for (int i = 0; i < SM; i++)
for (int j = 0; j < SM; j++)
b[i * SM + j] = a[i * n + j];
}
static void kernel(float *restrict a, float *restrict b, float *restrict c, int n)
{
for (int i = 0; i < SM; i++)
{
for (int k = 0; k < SM; k++)
{
for (int j = 0; j < SM; j++)
{
c[i * n + j] += a[i * n + k] * b[k * SM + j];
}
}
}
}
void gemm_accel(float *restrict a, float *restrict b, float *restrict c, int n)
{
int bk = n / SM;
float b2[SM * SM];
for (int i = 0; i < bk; i++)
{
for (int j = 0; j < bk; j++)
{
for (int k = 0; k < bk; k++)
{
reorder2(&b[SM * (k * n + j)], b2, n);
kernel(&a[SM * (i * n + k)], b2, &c[SM * (i * n + j)], n);
}
}
}
}
#pragma omp end declare target
void gemm_opt(float *restrict a, float *restrict b, float *restrict c, int n)
{
int bk = n / SM;
{
float b2[SM * SM];
for (int i = 0; i < bk; i++)
{
for (int j = 0; j < bk; j++)
{
for (int k = 0; k < bk; k++)
{
reorder2(&b[SM * (k * n + j)], b2, n);
kernel(&a[SM * (i * n + k)], b2, &c[SM * (i * n + j)], n);
}
}
}
}
}
void gemm(float *restrict a, float *restrict b, float *restrict c, int n)
{
int i, j, k;
for (int i = 0; i < n; ++i)
{
for (int j = 0; j < n; ++j)
{
float sum = 0.0;
for (int k = 0; k < n; ++k)
{
sum += a[i + k * n] * b[k + j * n];
}
c[i * n + j] += sum;
}
}
}
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float *a, *b, *c, *g;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (a = (float *)malloc(sizeof(*a) * n * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (b = (float *)malloc(sizeof(*b) * n * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (c = (float *)malloc(sizeof(*c) * n * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (NULL == (g = (float *)malloc(sizeof(*g) * n * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(a);
free(b);
free(c);
free(g);
exit(EXIT_FAILURE);
}
if (n <= 1024)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
}
if (n <= 4096)
{
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_opt(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("gemm_opt on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
}
clock_gettime(CLOCK_REALTIME, rt + 0);
gemm_accel(a, b, c, n);
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("GEMM-opt1 on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n * n * n / (1.0e6 * wt));
for (i = 0; i < n; i++)
{
iret = *(int *)(g + i) ^ *(int *)(c + i);
assert(iret == 0);
}
free(a);
free(b);
free(c);
free(g);
return 0;
}

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/**
* @file saxpy.c
*
* @brief saxpy performs the \c axpy computation in single-precision on both
* host and accelerator. The performance (in MFLOPS) on host and accelerator is
* compared and the numerical results are also verified for consistency.
*
* The \c axpy computation is defined as:
*
* y := a * x + y
*
* where:
*
* - a is a scalar.
* - x and y are vectors each with n elements.
*
* Please note that in this version only <em>one GPU thread</em> is used.
*
* Offload to GPU:
*
* gcc -fopenmp -foffload=nvptx-none saxpy.c
*
*/
#include <assert.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include <omp.h>
#include "utils.h"
#define TWO02 (1 << 2)
#define TWO04 (1 << 4)
#define TWO08 (1 << 8)
#ifndef N
#define N (1 << 26)
#endif
int main(int argc, char *argv[])
{
int i, n = N,
iret = 0;
float a = 101.0f / TWO02,
b, c,
*x, *y, *z;
struct timespec rt[2];
double wt; // walltime
if (argc > 1)
n = atoi(argv[1]);
/*
* 0. prepare x, y, and z
*
* y := a * x + y (on host)
* z := a * x + z (on accel)
*/
if (NULL == (x = (float *)malloc(sizeof(*x) * n)))
{
printf("error: memory allocation for 'x'\n");
iret = -1;
}
if (NULL == (y = (float *)malloc(sizeof(*y) * n)))
{
printf("error: memory allocation for 'y'\n");
iret = -1;
}
if (NULL == (z = (float *)malloc(sizeof(*z) * n)))
{
printf("error: memory allocation for 'z'\n");
iret = -1;
}
if (0 != iret)
{
free(x);
free(y);
free(z);
exit(EXIT_FAILURE);
}
b = rand() % TWO04;
c = rand() % TWO08;
for (i = 0; i < n; i++)
{
x[i] = b / (float)TWO02;
y[i] = z[i] = c / (float)TWO04;
}
/*
* 1. saxpy on host
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
for (i = 0; i < n; i++)
{
y[i] = a * x[i] + y[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on host : %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 2. saxpy on accel
*/
clock_gettime(CLOCK_REALTIME, rt + 0);
for (i = 0; i < n; i++)
{
z[i] = a * x[i] + z[i];
}
clock_gettime(CLOCK_REALTIME, rt + 1);
wt = (rt[1].tv_sec - rt[0].tv_sec) + 1.0e-9 * (rt[1].tv_nsec - rt[0].tv_nsec);
printf("saxpy on accel: %9.3f sec %9.1f MFLOPS\n", wt, 2.0 * n / (1.0e6 * wt));
/*
* 3. verify numerical consistency
*/
for (i = 0; i < n; i++)
{
iret = *(int *)(y + i) ^ *(int *)(z + i);
assert(iret == 0);
}
return 0;
}

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#!/bin/bash
module load clang/11.0.0 cuda/10.0

150
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/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file utils.c
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief File containing utilities functions for HPC Unimore Class
*
* Utilities for OpenMP lab.
*
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#define _POSIX_C_SOURCE 199309L
#include <time.h>
#include <limits.h>
#include <math.h>
#include <stdio.h>
#include <assert.h>
#include "utils.h"
#define MAX_ITERATIONS 100
static struct timespec timestampA, timestampB;
static unsigned long long statistics[MAX_ITERATIONS];
static int iterations = 0;
static unsigned long long __diff_ns(struct timespec start, struct timespec end)
{
struct timespec temp;
if ((end.tv_nsec - start.tv_nsec) < 0)
{
temp.tv_sec = end.tv_sec - start.tv_sec - 1;
temp.tv_nsec = 1000000000ULL + end.tv_nsec - start.tv_nsec;
}
else
{
temp.tv_sec = end.tv_sec - start.tv_sec;
temp.tv_nsec = end.tv_nsec - start.tv_nsec;
}
return temp.tv_nsec + temp.tv_sec * 1000000000ULL;
}
void start_timer()
{
asm volatile("" ::
: "memory");
clock_gettime(CLOCK_MONOTONIC_RAW, &timestampA);
asm volatile("" ::
: "memory");
}
void stop_timer()
{
unsigned long long elapsed = 0ULL;
asm volatile("" ::
: "memory");
clock_gettime(CLOCK_MONOTONIC_RAW, &timestampB);
asm volatile("" ::
: "memory");
}
unsigned long long elapsed_ns()
{
return __diff_ns(timestampA, timestampB);
}
void start_stats()
{
start_timer();
}
void collect_stats()
{
assert(iterations < MAX_ITERATIONS);
stop_timer();
statistics[iterations++] = elapsed_ns();
}
void print_stats()
{
unsigned long long min = ULLONG_MAX;
unsigned long long max = 0LL;
double average = 0.0;
double std_deviation = 0.0;
double sum = 0.0;
/* Compute the sum of all elements */
for (int i = 0; i < iterations; i++)
{
if (statistics[i] > max)
max = statistics[i];
if (statistics[i] < min)
min = statistics[i];
sum = sum + statistics[i] / 1E6;
}
average = sum / (double)iterations;
/* Compute variance and standard deviation */
for (int i = 0; i < iterations; i++)
{
sum = sum + pow((statistics[i] / 1E6 - average), 2);
}
std_deviation = sqrt(sum / (double)iterations);
printf("AvgTime\tMinTime\tMaxTime\tStdDev\n");
printf("%.4f ms\t%.4f ms\t%.4f ms\t%.4f\n", (double)average, (double)min / 1E6, (double)max / 1E6, (double)std_deviation);
}
#if defined(__GNUC__)
#pragma GCC push_options
#pragma GCC optimize("O0")
void work(unsigned long num)
#else
void work __attribute__((optnone)) (unsigned long num)
#endif
{
volatile int cnt = 0;
for (int i = 0; i < num; i++)
cnt += i;
}
#if defined(__GNUC__)
#pragma GCC pop_options
#endif

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/*
* BSD 2-Clause License
*
* Copyright (c) 2020, Alessandro Capotondi
* All rights reserved.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
*
* * Redistributions of source code must retain the above copyright notice, this
* list of conditions and the following disclaimer.
*
* * Redistributions in binary form must reproduce the above copyright notice,
* this list of conditions and the following disclaimer in the documentation
* and/or other materials provided with the distribution.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
* AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR
* SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,
* OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
* OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*/
/**
* @file utils.h
* @author Alessandro Capotondi
* @date 27 Mar 2020
* @brief File containing utilities functions for HPC Unimore Class
*
* The header define time functions and dummy workload used on the example tests.
*
* @see http://algo.ing.unimo.it/people/andrea/Didattica/HPC/index.html
*/
#ifndef __UTILS_H__
#define __UTILS_H__
#include <stdarg.h>
#if defined(VERBOSE)
#define DEBUG_PRINT(x, ...) printf((x), ##__VA_ARGS__)
#else
#define DEBUG_PRINT(x, ...)
#endif
#if !defined(NTHREADS)
#define NTHREADS (4)
#endif
#if !defined(NTHREADS_GPU)
#define NTHREADS_GPU (1024)
#endif
/**
* @brief The function set the timestampA
*
* The function is used to measure elapsed time between two execution points.
* The function start_timer() sets the starting point timestamp, while the function
* stop_timer() sets the termination timestamp. The elapsed time, expressed in nanoseconds,
* between the two points can be retrieved using the function elapsed_ns().
*
* Example usage:
* @code
* start_timer(); // Point A
* //SOME CODE HERE
* stop_timer(); // Point B
* printf("Elapsed time = %llu ns\n", elapsed_ns())); //Elapsed time between A and B
* //SOME OTHER CODE HERE
* stop_timer(); // Point C
* printf("Elapsed time = %llu ns\n", elapsed_ns())); //Elapsed time between A and C
* @endcode
*
* @return void
* @see start_timer()
* @see stop_timer()
* @see elapsed_ns()
*/
void start_timer();
/**
* @brief The function set the second timestamps
*
* The function is used to measure elapsed time between two execution points.
* The function start_timer() sets the starting point timestamp, while the function
* stop_timer() returns the elapsed time, expressed in nanoseconds between the last call
* of start_timer() and the current execution point.
*
* Example usage:
* @code
* start_timer(); // Point A
* //SOME CODE HERE
* stop_timer(); // Point B
* printf("Elapsed time = %llu ns\n", elapsed_ns())); //Elapsed time between A and B
* //SOME OTHER CODE HERE
* stop_timer(); // Point C
* printf("Elapsed time = %llu ns\n", elapsed_ns())); //Elapsed time between A and C
* @endcode
*
* @return void
* @see start_timer()
* @see stop_timer()
* @see elapsed_ns()
*/
void stop_timer();
/**
* @brief Elapsed nano seconds between start_timer() and stop_timer().
*
* @return Elapsed nano seconds
* @see start_timer()
* @see stop_timer()
*/
unsigned long long elapsed_ns();
/**
* @brief The function init the starting point of stat measurement.
*
* The function is similar to start_timer().
*
* @return void
* @see start_timer
*/
void start_stats();
/**
* @brief The function collects the elapsed time between the current exeuction point and the
* last call of start_stats().
*
* @return void
*/
void collect_stats();
/**
* @brief The function display the collected statistics.
* @return void
*/
void print_stats();
/**
* @brief The dummy work function
*
* The function is used to emulate some usefull workload.
*
* @param @num work duration in terms of loop iterations.
* @return void
*/
#if defined(__GNUC__)
#pragma GCC push_options
#pragma GCC optimize("O0")
void work(unsigned long num);
#else
void work __attribute__((optnone)) (unsigned long num);
#endif
#if defined(__GNUC__)
#pragma GCC pop_options
#endif
#endif /*__UTILS_H__*/