demos/mandelbrot/mandelbrot.cpp - eigen - Git at Google

 // 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"
	// 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"