eigen/demos/mandelbrot/mandelbrot.cpp

// This file is part of Eigen, a lightweight C++ template library
// for linear algebra.
//
// Copyright (C) 2008 Benoit Jacob <jacob.benoit.1@gmail.com>
//
// This Source Code Form is subject to the terms of the Mozilla
// Public License v. 2.0. If a copy of the MPL was not distributed
// with this file, You can obtain one at http://mozilla.org/MPL/2.0/.

#include "mandelbrot.h"
#include <iostream>
#include <QtGui/QPainter>
#include <QtGui/QImage>
#include <QtGui/QMouseEvent>
#include <QtCore/QTime>

void MandelbrotWidget::resizeEvent(QResizeEvent *) {
  if (size < width() * height()) {
    std::cout << "reallocate buffer" << std::endl;
    size = width() * height();
    if (buffer) delete[] buffer;
    buffer = new unsigned char[4 * size];
  }
}

template <typename T>
struct iters_before_test {
  enum { ret = 8 };
};
template <>
struct iters_before_test<double> {
  enum { ret = 16 };
};

template <typename Real>
void MandelbrotThread::render(int img_width, int img_height) {
  enum { packetSize = Eigen::internal::packet_traits<Real>::size };  // number of reals in a Packet
  typedef Eigen::Array<Real, packetSize, 1> Packet;                  // wrap a Packet as a vector

  enum { iters_before_test = iters_before_test<Real>::ret };
  max_iter = (max_iter / iters_before_test) * iters_before_test;
  const int alignedWidth = (img_width / packetSize) * packetSize;
  unsigned char *const buffer = widget->buffer;
  const double xradius = widget->xradius;
  const double yradius = xradius * img_height / img_width;
  const int threadcount = widget->threadcount;
  typedef Eigen::Array<Real, 2, 1> Vector2;
  Vector2 start(widget->center.x() - widget->xradius, widget->center.y() - yradius);
  Vector2 step(2 * widget->xradius / img_width, 2 * yradius / img_height);
  total_iter = 0;

  for (int y = id; y < img_height; y += threadcount) {
    int pix = y * img_width;

    // for each pixel, we're going to do the iteration z := z^2 + c where z and c are complex numbers,
    // starting with z = c = complex coord of the pixel. pzi and pzr denote the real and imaginary parts of z.
    // pci and pcr denote the real and imaginary parts of c.

    Packet pzi_start, pci_start;
    for (int i = 0; i < packetSize; i++) pzi_start[i] = pci_start[i] = start.y() + y * step.y();

    for (int x = 0; x < alignedWidth; x += packetSize, pix += packetSize) {
      Packet pcr, pci = pci_start, pzr, pzi = pzi_start, pzr_buf;
      for (int i = 0; i < packetSize; i++) pzr[i] = pcr[i] = start.x() + (x + i) * step.x();

      // do the iterations. Every iters_before_test iterations we check for divergence,
      // in which case we can stop iterating.
      int j = 0;
      typedef Eigen::Matrix<int, packetSize, 1> Packeti;
      Packeti pix_iter = Packeti::Zero(),  // number of iteration per pixel in the packet
          pix_dont_diverge;                // whether or not each pixel has already diverged
      do {
        for (int i = 0; i < iters_before_test / 4; i++)  // peel the inner loop by 4
        {
#define ITERATE              \
  pzr_buf = pzr;             \
  pzr = pzr.square();        \
  pzr -= pzi.square();       \
  pzr += pcr;                \
  pzi = (2 * pzr_buf) * pzi; \
  pzi += pci;
          ITERATE ITERATE ITERATE ITERATE
        }
        pix_dont_diverge =
            ((pzr.square() + pzi.square()).eval()  // temporary fix as what follows is not yet vectorized by Eigen
             <= Packet::Constant(4))
                // the 4 here is not a magic value, it's a math fact that if
                // the square modulus is >4 then divergence is inevitable.
                .template cast<int>();
        pix_iter += iters_before_test * pix_dont_diverge;
        j++;
        total_iter += iters_before_test * packetSize;
      } while (j < max_iter / iters_before_test && pix_dont_diverge.any());  // any() is not yet vectorized by Eigen

      // compute pixel colors
      for (int i = 0; i < packetSize; i++) {
        buffer[4 * (pix + i)] = 255 * pix_iter[i] / max_iter;
        buffer[4 * (pix + i) + 1] = 0;
        buffer[4 * (pix + i) + 2] = 0;
      }
    }

    // if the width is not a multiple of packetSize, fill the remainder in black
    for (int x = alignedWidth; x < img_width; x++, pix++)
      buffer[4 * pix] = buffer[4 * pix + 1] = buffer[4 * pix + 2] = 0;
  }
  return;
}

void MandelbrotThread::run() {
  setTerminationEnabled(true);
  double resolution = widget->xradius * 2 / widget->width();
  max_iter = 128;
  if (resolution < 1e-4f) max_iter += 128 * (-4 - std::log10(resolution));
  int img_width = widget->width() / widget->draft;
  int img_height = widget->height() / widget->draft;
  single_precision = resolution > 1e-7f;

  if (single_precision)
    render<float>(img_width, img_height);
  else
    render<double>(img_width, img_height);
}

void MandelbrotWidget::paintEvent(QPaintEvent *) {
  static float max_speed = 0;
  long long total_iter = 0;

  QTime time;
  time.start();
  for (int th = 0; th < threadcount; th++) threads[th]->start(QThread::LowPriority);
  for (int th = 0; th < threadcount; th++) {
    threads[th]->wait();
    total_iter += threads[th]->total_iter;
  }
  int elapsed = time.elapsed();

  if (draft == 1) {
    float speed = elapsed ? float(total_iter) * 1000 / elapsed : 0;
    max_speed = std::max(max_speed, speed);
    std::cout << threadcount << " threads, " << elapsed << " ms, " << speed << " iters/s (max " << max_speed << ")"
              << std::endl;
    int packetSize = threads[0]->single_precision ? int(Eigen::internal::packet_traits<float>::size)
                                                  : int(Eigen::internal::packet_traits<double>::size);
    setWindowTitle(
        QString("resolution ") + QString::number(xradius * 2 / width(), 'e', 2) +
        QString(", %1 iterations per pixel, ").arg(threads[0]->max_iter) +
        (threads[0]->single_precision ? QString("single ") : QString("double ")) + QString("precision, ") +
        (packetSize == 1 ? QString("no vectorization") : QString("vectorized (%1 per packet)").arg(packetSize)));
  }

  QImage image(buffer, width() / draft, height() / draft, QImage::Format_RGB32);
  QPainter painter(this);
  painter.drawImage(QPoint(0, 0), image.scaled(width(), height()));

  if (draft > 1) {
    draft /= 2;
    setWindowTitle(QString("recomputing at 1/%1 resolution...").arg(draft));
    update();
  }
}

void MandelbrotWidget::mousePressEvent(QMouseEvent *event) {
  if (event->buttons() & Qt::LeftButton) {
    lastpos = event->pos();
    double yradius = xradius * height() / width();
    center = Eigen::Vector2d(center.x() + (event->pos().x() - width() / 2) * xradius * 2 / width(),
                             center.y() + (event->pos().y() - height() / 2) * yradius * 2 / height());
    draft = 16;
    for (int th = 0; th < threadcount; th++) threads[th]->terminate();
    update();
  }
}

void MandelbrotWidget::mouseMoveEvent(QMouseEvent *event) {
  QPoint delta = event->pos() - lastpos;
  lastpos = event->pos();
  if (event->buttons() & Qt::LeftButton) {
    double t = 1 + 5 * double(delta.y()) / height();
    if (t < 0.5) t = 0.5;
    if (t > 2) t = 2;
    xradius *= t;
    draft = 16;
    for (int th = 0; th < threadcount; th++) threads[th]->terminate();
    update();
  }
}

int main(int argc, char *argv[]) {
  QApplication app(argc, argv);
  MandelbrotWidget w;
  w.show();
  return app.exec();
}

#include "mandelbrot.moc"