Matrix &operator=(const T &val) {
V vec(val);
for (unsigned int i = 0; i < m_mem.vectorsCount(); ++i) {
m_mem.vector(i) = vec;
}
return *this;
}
Matrix &operator+=(const Matrix &rhs) {
for (unsigned int i = 0; i < m_mem.vectorsCount(); ++i) {
V v1(m_mem.vector(i));
v1 += V(rhs.m_mem.vector(i));
m_mem.vector(i) = v1;
}
return *this;
}
int main()
{
{
float_v x_i(float_v::IndexType::IndexesFromZero());
for ( unsigned int i = 0; i < x_points.vectorsCount(); ++i, x_i += float_v::Size ) {
const float_v x = x_i * h;
x_points.vector(i) = x;
y_points.vector(i) = fu(x);
}
}
dy_points = Vc::malloc<float, Vc::AlignOnVector>(N + float_v::Size - 1) + (float_v::Size - 1);
double speedup;
TimeStampCounter timer;
{ ///////// ignore this part - it only wakes up the CPU ////////////////////////////
const float oneOver2h = 0.5f / h;
// set borders explicit as up- or downdifferential
dy_points[0] = (y_points[1] - y_points[0]) / h;
// GCC auto-vectorizes the following loop. It is interesting to see that both Vc::Scalar and
// Vc::SSE are faster, though.
for ( int i = 1; i < N - 1; ++i) {
dy_points[i] = (y_points[i + 1] - y_points[i - 1]) * oneOver2h;
}
dy_points[N - 1] = (y_points[N - 1] - y_points[N - 2]) / h;
} //////////////////////////////////////////////////////////////////////////////////
{
std::cout << "\n" << std::setw(60) << "Classical finite difference method" << std::endl;
timer.Start();
const float oneOver2h = 0.5f / h;
// set borders explicit as up- or downdifferential
dy_points[0] = (y_points[1] - y_points[0]) / h;
// GCC auto-vectorizes the following loop. It is interesting to see that both Vc::Scalar and
// Vc::SSE are faster, though.
for ( int i = 1; i < N - 1; ++i) {
dy_points[i] = (y_points[i + 1] - y_points[i - 1]) * oneOver2h;
}
dy_points[N - 1] = (y_points[N - 1] - y_points[N - 2]) / h;
timer.Stop();
printResults();
std::cout << "cycle count: " << timer.Cycles()
<< " | " << static_cast<double>(N * 2) / timer.Cycles() << " FLOP/cycle"
<< " | " << static_cast<double>(N * 2 * sizeof(float)) / timer.Cycles() << " Byte/cycle"
<< "\n";
}
speedup = timer.Cycles();
{
std::cout << std::setw(60) << "Vectorized finite difference method" << std::endl;
timer.Start();
// All the differentials require to calculate (r - l) / 2h, where we calculate 1/2h as a
// constant before the loop to avoid unnecessary calculations. Note that a good compiler can
// already do this for you.
const float_v oneOver2h = 0.5f / h;
// Calculate the left border
dy_points[0] = (y_points[1] - y_points[0]) / h;
// Calculate the differentials streaming through the y and dy memory. The picture below
// should give an idea of what values in y get read and what values are written to dy in
// each iteration:
//
// y [...................................]
// 00001111222233334444555566667777
// 00001111222233334444555566667777
// dy [...................................]
// 00001111222233334444555566667777
//
// The loop is manually unrolled four times to improve instruction level parallelism and
// prefetching on architectures where four vectors fill one cache line. (Note that this
// unrolling breaks auto-vectorization of the Vc::Scalar implementation when compiling with
// GCC.)
for (unsigned int i = 0; i < (y_points.entriesCount() - 2) / float_v::Size; i += 4) {
// Prefetches make sure the data which is going to be used in 24/4 iterations is already
// in the L1 cache. The prefetchForOneRead additionally instructs the CPU to not evict
// these cache lines to L2/L3.
Vc::prefetchForOneRead(&y_points[(i + 24) * float_v::Size]);
// calculate float_v::Size differentials per (left - right) / 2h
const float_v dy0 = (y_points.vector(i + 0, 2) - y_points.vector(i + 0)) * oneOver2h;
const float_v dy1 = (y_points.vector(i + 1, 2) - y_points.vector(i + 1)) * oneOver2h;
const float_v dy2 = (y_points.vector(i + 2, 2) - y_points.vector(i + 2)) * oneOver2h;
const float_v dy3 = (y_points.vector(i + 3, 2) - y_points.vector(i + 3)) * oneOver2h;
// Use streaming stores to reduce the required memory bandwidth. Without streaming
// stores the CPU would first have to load the cache line, where the store occurs, from
// memory into L1, then overwrite the data, and finally write it back to memory. But
// since we never actually need the data that the CPU fetched from memory we'd like to
// keep that bandwidth free for real work. Streaming stores allow us to issue stores
// which the CPU gathers in store buffers to form full cache lines, which then get
// written back to memory directly without the costly read. Thus we make better use of
// the available memory bandwidth.
dy0.store(&dy_points[(i + 0) * float_v::Size + 1], Vc::Streaming);
dy1.store(&dy_points[(i + 1) * float_v::Size + 1], Vc::Streaming);
dy2.store(&dy_points[(i + 2) * float_v::Size + 1], Vc::Streaming);
dy3.store(&dy_points[(i + 3) * float_v::Size + 1], Vc::Streaming);
}
// Process the last vector. Note that this works for any N because Vc::Memory adds padding
// to y_points and dy_points such that the last scalar value is somewhere inside lastVector.
// The correct right border value for dy_points is overwritten in the last step unless N is
// a multiple of float_v::Size + 2.
// y [...................................]
// 8888
// 8888
// dy [...................................]
// 8888
{
const size_t i = y_points.vectorsCount() - 1;
const float_v left = y_points.vector(i, -2);
const float_v right = y_points.lastVector();
((right - left) * oneOver2h).store(&dy_points[i * float_v::Size - 1], Vc::Unaligned);
}
// ... and finally the right border
dy_points[N - 1] = (y_points[N - 1] - y_points[N - 2]) / h;
timer.Stop();
printResults();
std::cout << "cycle count: " << timer.Cycles()
<< " | " << static_cast<double>(N * 2) / timer.Cycles() << " FLOP/cycle"
<< " | " << static_cast<double>(N * 2 * sizeof(float)) / timer.Cycles() << " Byte/cycle"
<< "\n";
}
speedup /= timer.Cycles();
std::cout << "Speedup: " << speedup << "\n";
Vc::free(dy_points - float_v::Size + 1);
return 0;
}