template <size_t N, typename F> Vc_ALWAYS_INLINE void benchmark(F &&f)
{
TimeStampCounter tsc;
auto cycles = tsc.cycles();
cycles = 0x7fffffff;
for (int i = 0; i < 100; ++i) {
tsc.start();
for (int j = 0; j < 10; ++j) {
auto C = f();
unused(C);
}
tsc.stop();
cycles = std::min(cycles, tsc.cycles());
}
//std::cout << cycles << " Cycles for " << N *N *(N + N - 1) << " FLOP => ";
std::cout << std::setw(19) << std::setprecision(3)
<< double(N * N * (N + N - 1) * 10) / cycles;
//<< " FLOP/cycle (" << variant << ")\n";
}
void MandelBase::run()
{
while (!m_abort) {
// first we copy the parameters to our local data so that the main main thread can give a
// new task while we're working
m_mutex.lock();
// destination image, RGB is good - no need for alpha
QImage image(m_size, QImage::Format_RGB32);
float x = m_x;
float y = m_y;
float scale = m_scale;
m_mutex.unlock();
// benchmark the number of cycles it takes
TimeStampCounter timer;
timer.Start();
// calculate the mandelbrot set/image
mandelMe(image, x, y, scale, 255);
timer.Stop();
// if no new set was requested in the meantime - return the finished image
if (!m_restart) {
emit ready(image, timer.Cycles());
}
// wait for more work
m_mutex.lock();
if (!m_restart) {
m_wait.wait(&m_mutex);
}
m_restart = false;
m_mutex.unlock();
}
}
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;
}
void Baker::createImage()
{
const int iHeight = m_image.height();
const int iWidth = m_image.width();
// Parameters Begin
const float S = 4.f;
const float nSteps[2] = {
static_cast<float>(m_opt.steps[0] == -1 ? std::sqrt(iWidth) * iWidth : m_opt.steps[0]),
static_cast<float>(m_opt.steps[1] == -1 ? std::sqrt(iHeight) * iHeight : m_opt.steps[1])
};
const int upperBound[3] = { m_opt.red[1], m_opt.green[1], m_opt.blue[1] };
const int lowerBound[3] = { m_opt.red[0], m_opt.green[0], m_opt.blue[0] };
int overallLowerBound = m_opt.it[0];
int maxIterations = m_opt.it[1];// maxOf(maxOf(overallLowerBound, upperBound[0]), maxOf(upperBound[1], upperBound[2]));
float realMin = -2.102613f;
float realMax = 1.200613f;
float imagMin = 0.f;
float imagMax = 1.23971f;
// Parameters End
TimeStampCounter timer;
timer.start();
// helper constants
const int overallUpperBound = maxOf(upperBound[0], maxOf(upperBound[1], upperBound[2]));
const float maxX = static_cast<float>(iWidth ) - 1.f;
const float maxY = static_cast<float>(iHeight) - 1.f;
const float xFact = iWidth / m_width;
const float yFact = iHeight / m_height;
const float realStep = (realMax - realMin) / nSteps[0];
const float imagStep = (imagMax - imagMin) / nSteps[1];
Canvas canvas(iHeight, iWidth);
#ifdef Scalar
for (float real = realMin; real <= realMax; real += realStep) {
m_progress.setValue(99.f * (real - realMin) / (realMax - realMin));
for (float imag = imagMin; imag <= imagMax; imag += imagStep) {
Z c(real, imag);
Z c2 = Z(1.08f * real + 0.15f, imag);
if (fastNorm(Z(real + 1.f, imag)) < 0.06f || (std::real(c2) < 0.42f && fastNorm(c2) < 0.417f)) {
continue;
}
Z z = c;
int n;
for (n = 0; n <= maxIterations && fastNorm(z) < S; ++n) {
z = P(z, c);
}
if (n <= maxIterations && n >= overallLowerBound) {
// point is outside of the Mandelbrot set and required enough (overallLowerBound)
// iterations to reach the cut-off value S
Z cn(real, -imag);
Z zn = cn;
z = c;
for (int i = 0; i <= overallUpperBound; ++i) {
const float y2 = (std::imag(z) - m_y) * yFact;
const float yn2 = (std::imag(zn) - m_y) * yFact;
if (y2 >= 0.f && y2 < maxY && yn2 >= 0.f && yn2 < maxY) {
const float x2 = (std::real(z) - m_x) * xFact;
if (x2 >= 0.f && x2 < maxX) {
const int red = (i >= lowerBound[0] && i <= upperBound[0]) ? 1 : 0;
const int green = (i >= lowerBound[1] && i <= upperBound[1]) ? 1 : 0;
const int blue = (i >= lowerBound[2] && i <= upperBound[2]) ? 1 : 0;
canvas.addDot(x2, y2 , red, green, blue);
canvas.addDot(x2, yn2, red, green, blue);
}
}
z = P(z, c);
zn = P(zn, cn);
if (fastNorm(z) >= S) { // optimization: skip some useless looping
break;
}
}
}
}
}
#else
const float imagStep2 = imagStep * float_v::Size;
const float_v imagMin2 = imagMin + imagStep * static_cast<float_v>(int_v::IndexesFromZero());
for (float real = realMin; real <= realMax; real += realStep) {
m_progress.setValue(99.f * (real - realMin) / (realMax - realMin));
for (float_v imag = imagMin2; all_of(imag <= imagMax); imag += imagStep2) {
// FIXME: extra "tracks" if nSteps[1] is not a multiple of float_v::Size
Z c(float_v(real), imag);
Z c2 = Z(float_v(1.08f * real + 0.15f), imag);
if (all_of(fastNorm(Z(float_v(real + 1.f), imag)) < 0.06f ||
(std::real(c2) < 0.42f && fastNorm(c2) < 0.417f))) {
continue;
}
Z z = c;
int_v n(Vc::Zero);
int_m inside = fastNorm(z) < S;
while (!(inside && n <= maxIterations).isEmpty()) {
z = P(z, c);
++n(inside);
inside &= fastNorm(z) < S;
}
inside |= n < overallLowerBound;
if (inside.isFull()) {
continue;
}
Z cn(float_v(real), -imag);
Z zn = cn;
z = c;
for (int i = 0; i <= overallUpperBound; ++i) {
const float_v y2 = (std::imag(z) - m_y) * yFact;
const float_v yn2 = (std::imag(zn) - m_y) * yFact;
const float_v x2 = (std::real(z) - m_x) * xFact;
z = P(z, c);
zn = P(zn, cn);
const float_m drawMask = !inside && y2 >= 0.f && x2 >= 0.f && y2 < maxY && x2 < maxX && yn2 >= 0.f && yn2 < maxY;
const int red = (i >= lowerBound[0] && i <= upperBound[0]) ? 1 : 0;
const int green = (i >= lowerBound[1] && i <= upperBound[1]) ? 1 : 0;
const int blue = (i >= lowerBound[2] && i <= upperBound[2]) ? 1 : 0;
for(int j : where(drawMask)) {
canvas.addDot(x2[j], y2 [j], red, green, blue);
canvas.addDot(x2[j], yn2[j], red, green, blue);
}
if (all_of(fastNorm(z) >= S)) { // optimization: skip some useless looping
break;
}
}
}
}
#endif
canvas.toQImage(&m_image);
timer.stop();
m_progress.done();
qDebug() << timer.cycles() << "cycles";
if (m_filename.isEmpty()) {
m_filename = QString("r%1-%2_g%3-%4_b%5-%6_s%7-%8_i%9-%10_%11x%12.png")
.arg(lowerBound[0]).arg(upperBound[0])
.arg(lowerBound[1]).arg(upperBound[1])
.arg(lowerBound[2]).arg(upperBound[2])
.arg(nSteps[0]).arg(nSteps[1])
.arg(overallLowerBound).arg(maxIterations)
.arg(m_image.width()).arg(m_image.height());
}
m_image.save(m_filename);
}