Add SYCL port

Makefile

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+
+CXX=clang++ --gcc-toolchain=/nfs/software/x86_64/gcc/7.4.0
+CFLAGS=-std=c++11 -O3 -fsycl
+LIBS=-lOpenCL
+
+heat: heat_sycl.cpp Makefile
+	$(CXX) $(CFLAGS) heat_sycl.cpp $(LIBS) -o $@
+
+

heat_sycl.cpp

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+
+/*
+** PROGRAM: heat equation solve
+**
+** PURPOSE: This program will explore use of an explicit
+**          finite difference method to solve the heat
+**          equation under a method of manufactured solution (MMS)
+**          scheme. The solution has been set to be a simple 
+**          function based on exponentials and trig functions.
+**
+**          A finite difference scheme is used on a 1000x1000 cube.
+**          A total of 0.5 units of time are simulated.
+**
+**          The MMS solution has been adapted from
+**          G.W. Recktenwald (2011). Finite difference approximations
+**          to the Heat Equation. Portland State University.
+**
+**
+** USAGE:   Run with two arguments:
+**          First is the number of cells.
+**          Second is the number of timesteps.
+**
+**          For example, with 100x100 cells and 10 steps:
+**
+**          ./heat 100 10
+**
+**
+** HISTORY: Written by Tom Deakin, Oct 2018
+**          Ported to SYCL by Tom Deakin, Nov 2019
+**
+*/
+
+#include <iostream>
+#include <chrono>
+#include <cmath>
+
+#include <CL/sycl.hpp>
+
+// Key constants used in this program
+#define PI cl::sycl::acos(-1.0) // Pi
+#define LINE "--------------------" // A line for fancy output
+
+// Function definitions
+void initial_value(cl::sycl::queue &queue, const unsigned int n, const double dx, const double length, cl::sycl::buffer<double,2>& u);
+void zero(cl::sycl::queue &queue, const unsigned int n, cl::sycl::buffer<double,2>& u);
+void solve(cl::sycl::queue &queue, const unsigned int n, const double alpha, const double dx, const double dt, cl::sycl::buffer<double,2>& u, cl::sycl::buffer<double,2>& u_tmp);
+double solution(const double t, const double x, const double y, const double alpha, const double length);
+double l2norm(const unsigned int n, const double * u, const int nsteps, const double dt, const double alpha, const double dx, const double length);
+
+// Main function
+int main(int argc, char *argv[]) {
+
+  // Start the total program runtime timer
+  auto start = std::chrono::high_resolution_clock::now();
+
+  // Problem size, forms an nxn grid
+  unsigned int n = 1000;
+
+  // Number of timesteps
+  int nsteps = 10;
+
+
+  // Check for the correct number of arguments
+  // Print usage and exits if not correct
+  if (argc == 3) {
+
+    // Set problem size from first argument
+    n = atoi(argv[1]);
+    if (n < 0) {
+      std::cerr << "Error: n must be positive" << std::endl;
+      exit(EXIT_FAILURE);
+    }
+
+    // Set number of timesteps from second argument
+    nsteps = atoi(argv[2]);
+    if (nsteps < 0) {
+      std::cerr << "Error: nsteps must be positive" << std::endl;
+      exit(EXIT_FAILURE);
+    }
+  }
+
+
+  //
+  // Set problem definition
+  //
+  double alpha = 0.1;          // heat equation coefficient
+  double length = 1000.0;      // physical size of domain: length x length square
+  double dx = length / (n+1);  // physical size of each cell (+1 as don't simulate boundaries as they are given)
+  double dt = 0.5 / nsteps;    // time interval (total time of 0.5s)
+
+
+  // Stability requires that dt/(dx^2) <= 0.5,
+  double r = alpha * dt / (dx * dx);
+
+  // Initalise SYCL queue on a GPU device
+  cl::sycl::queue queue {cl::sycl::gpu_selector{}};
+
+  // Print message detailing runtime configuration
+  std::cout
+    << std::endl
+    << " MMS heat equation" << std::endl << std::endl
+    << LINE << std::endl
+    << "Problem input" << std::endl << std::endl
+    << " Grid size: " << n << " x " << n << std::endl
+    << " Cell width: " << dx << std::endl
+    << " Grid length: " << length << "x" << length << std::endl
+    << std::endl
+    << " Alpha: " << alpha << std::endl
+    << std::endl
+    << " Steps: " <<  nsteps << std::endl
+    << " Total time: " << dt*(double)nsteps << std::endl
+    << " Time step: " << dt << std::endl
+    << " SYCL device: " << queue.get_device().get_info<cl::sycl::info::device::name>() << std::endl
+    << LINE << std::endl;
+
+  // Stability check
+  std::cout << "Stability" << std::endl << std::endl;
+  std::cout << " r value: " << r << std::endl;
+  if (r > 0.5)
+    std::cout << " Warning: unstable" << std::endl;
+  std::cout << LINE << std::endl;
+
+
+  // Allocate two nxn grids
+  cl::sycl::buffer<double, 2> u{cl::sycl::range<2>{n,n}};
+  cl::sycl::buffer<double, 2> u_tmp{cl::sycl::range<2>{n,n}};
+
+  // Set the initial value of the grid under the MMS scheme
+  initial_value(queue, n, dx, length, u);
+  zero(queue, n, u_tmp);
+
+  // Ensure everything is initalised on the device
+  queue.wait();
+
+  //
+  // Run through timesteps under the explicit scheme
+  //
+
+  // Start the solve timer
+  auto tic = std::chrono::high_resolution_clock::now();
+  for (int t = 0; t < nsteps; ++t) {
+
+    // Call the solve kernel
+    // Computes u_tmp at the next timestep
+    // given the value of u at the current timestep
+    solve(queue, n, alpha, dx, dt, u, u_tmp);
+
+    // Pointer swap
+    auto tmp = std::move(u);
+    u = std::move(u_tmp);
+    u_tmp = std::move(tmp);
+  }
+  // Stop solve timer
+  queue.wait();
+  auto toc = std::chrono::high_resolution_clock::now();
+
+  // Get access to u on the host
+  double *u_host = u.get_access<cl::sycl::access::mode::read>().get_pointer();
+
+  //
+  // Check the L2-norm of the computed solution
+  // against the *known* solution from the MMS scheme
+  //
+  double norm = l2norm(n, u_host, nsteps, dt, alpha, dx, length);
+
+  // Stop total timer
+  auto stop = std::chrono::high_resolution_clock::now();
+
+  // Print results
+  std::cout
+    << "Results" << std::endl << std::endl
+    << "Error (L2norm): " << norm << std::endl
+    << "Solve time (s): " << std::chrono::duration_cast<std::chrono::duration<double>>(toc-tic).count() << std::endl
+    << "Total time (s): " << std::chrono::duration_cast<std::chrono::duration<double>>(stop-start).count() << std::endl
+    << "Bandwidth (GB/s): " << 1.0E-9*2.0*n*n*nsteps*sizeof(double)/std::chrono::duration_cast<std::chrono::duration<double>>(toc-tic).count() << std::endl
+    << LINE << std::endl;
+
+}
+
+
+// Sets the mesh to an initial value, determined by the MMS scheme
+void initial_value(cl::sycl::queue& queue, const unsigned int n, const double dx, const double length, cl::sycl::buffer<double,2>& u) {
+
+  queue.submit([&](cl::sycl::handler& cgh) {
+    auto ua = u.get_access<cl::sycl::access::mode::discard_write>(cgh);
+
+    cgh.parallel_for<class initial_value_kernel>(cl::sycl::range<2>{n, n}, [=](cl::sycl::id<2> idx) {
+      int i = idx[1];
+      int j = idx[0];
+      double y = dx * (j+1); // Physical y position
+      double x = dx * (i+1); // Physical x position
+      ua[j][i] = cl::sycl::sin(PI * x / length) * cl::sycl::sin(PI * y / length);
+    });
+  });
+}
+
+
+// Zero the array u
+void zero(cl::sycl::queue& queue, const unsigned int n, cl::sycl::buffer<double,2>& u) {
+
+  queue.submit([&](cl::sycl::handler& cgh) {
+    auto ua = u.get_access<cl::sycl::access::mode::discard_write>(cgh);
+
+    cgh.parallel_for<class zero_kernel>(cl::sycl::range<2>{n,n}, [=](cl::sycl::id<2> idx) {
+      ua[idx] = 0.0;
+    });
+  });
+
+}
+
+
+// Compute the next timestep, given the current timestep
+void solve(cl::sycl::queue& queue, const unsigned int n, const double alpha, const double dx, const double dt, cl::sycl::buffer<double,2>& u_b, cl::sycl::buffer<double,2>& u_tmp_b) {
+
+  // Finite difference constant multiplier
+  const double r = alpha * dt / (dx * dx);
+  const double r2 = 1.0 - 4.0*r;
+
+  queue.submit([&](cl::sycl::handler& cgh) {
+    auto u_tmp = u_tmp_b.get_access<cl::sycl::access::mode::discard_write>(cgh);
+    auto u = u_b.get_access<cl::sycl::access::mode::read>(cgh);
+
+    // Loop over the nxn grid
+    cgh.parallel_for<class solve_kernel>(cl::sycl::range<2>{n, n}, [=](cl::sycl::id<2> idx) {
+      int j = idx[0];
+      int i = idx[1];
+
+      // Update the 5-point stencil, using boundary conditions on the edges of the domain.
+      // Boundaries are zero because the MMS solution is zero there.
+      u_tmp[j][i] =  r2 * u[j][i] +
+      r * ((i < n-1) ? u[j][i+1] : 0.0) +
+      r * ((i > 0)   ? u[j][i-1] : 0.0) +
+      r * ((j < n-1) ? u[j+1][i] : 0.0) +
+      r * ((j > 0)   ? u[j-1][i] : 0.0);
+    });
+  });
+}
+
+
+// True answer given by the manufactured solution
+double solution(const double t, const double x, const double y, const double alpha, const double length) {
+
+  return exp(-2.0*alpha*PI*PI*t/(length*length)) * sin(PI*x/length) * sin(PI*y/length);
+
+}
+
+
+// Computes the L2-norm of the computed grid and the MMS known solution
+// The known solution is the same as the boundary function.
+double l2norm(const unsigned int n, const double * u, const int nsteps, const double dt, const double alpha, const double dx, const double length) {
+
+  // Final (real) time simulated
+  double time = dt * (double)nsteps;
+
+  // L2-norm error
+  double l2norm = 0.0;
+
+  // Loop over the grid and compute difference of computed and known solutions as an L2-norm
+  double y = dx;
+  for (int j = 0; j < n; ++j) {
+    double x = dx;
+    for (int i = 0; i < n; ++i) {
+      double answer = solution(time, x, y, alpha, length);
+      l2norm += (u[i+j*n] - answer) * (u[i+j*n] - answer);
+
+      x += dx;
+    }
+    y += dx;
+  }
+
+  return sqrt(l2norm);
+
+}
+