Mandelbrot
The main goal of this work is to generate the Mandelbrot Set using different approaches: Sequential, Pthreads, OpenMP, OpenMPI and Cuda.
Install / Use
/learn @carloselcastro/MandelbrotREADME
Mandelbrot Set
This repository contains some of programs-exercises of class MAC5742 - Introduction to Concurrent, Parallel and Distributed Programming (2020) - Institute of Mathematics and Statistics, São Paulo University (IME-USP).
Members
Carlos Eduardo Leal de Castro - o/
Goal
The main goal of this work was to generate the Mandelbrot Set using different approaches: Sequential, Pthreads, OpenMP, OpenMPI and Cuda.
The Mandelbrot Set is the set of all complex points <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;$\mathbb{C}$" target="_blank"><img src="https://latex.codecogs.com/png.latex?\inline&space;$\mathbb{C}$" title="$\mathbb{C}$" /></a> such that the sequence <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;\{z_n\}_{n&space;\in&space;(\mathbb{N}&space;\cup&space;\{0\})}" target="_blank"><img src="https://latex.codecogs.com/png.latex?\inline&space;\{z_n\}_{n&space;\in&space;(\mathbb{N}&space;\cup&space;\{0\})}" title="\{z_n\}_{n \in (\mathbb{N} \cup \{0\})}" /></a>, given by <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;z_{n+1}&space;=&space;z_n^2&space;+&space;c," target="_blank"><img src="https://latex.codecogs.com/png.latex?\inline&space;z_{n+1}&space;=&space;z_n^2&space;+&space;c," title="z_{n+1} = z_n^2 + c," /></a> where <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;z_0&space;=&space;c&space;\in&space;\mathbb{C}\text{&space;and&space;}\mathbb{N}&space;\cup&space;\{0\}&space;=&space;\{0,1,2,3,4,\dots\}" target="_blank"><img src="https://latex.codecogs.com/png.latex?\inline&space;z_0&space;=&space;c&space;\in&space;\mathbb{C}\text{&space;and&space;}\mathbb{N}&space;\cup&space;\{0\}&space;=&space;\{0,1,2,3,4,\dots\}" title="z_0 = c \in \mathbb{C}\text{ and }\mathbb{N} \cup \{0\} = \{0,1,2,3,4,\dots\}" /></a> remains bounded.That is, for any <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;$z&space;\in&space;\mathbb{C}$" target="_blank"><img src="https://latex.codecogs.com/png.latex?\inline&space;$z&space;\in&space;\mathbb{C}$" title="$z \in \mathbb{C}$" /></a> that remains on this set, there exists a <a href="https://www.codecogs.com/eqnedit.php?latex=\inline&space;R_{max}\text{&space;such&space;that&space;}\vert&space;z&space;\vert&space;\leq&space;R_{max}." target="_blank"><img src="https://latex.codecogs.com/png.latex?\inline&space;R_{max}\text{&space;such&space;that&space;}\vert&space;z&space;\vert&space;\leq&space;R_{max}." title="R_{max}\text{ such that }\vert z \vert \leq R_{max}." /></a>
Performance tests
We performed some performance tests to compare all the methods used here: sequential, pthreads, openmp, openmpi, cuda, openmpi+openmp and openmpi+cuda. In these experiments, we measure the average time of 15 executions on each method, varying 3 different parameters:
- Dimensions (x,y) of grid and blocks (CUDA);
- Number of Threads (Pthreads and OMP);
- Number of processes (OMPI).
Algorithm | Executions --------- | ---------- Sequential | --- OpenMP | 2^0 to 2^10 threads Pthreads | 2^0 to 2^10 threads CUDA | 2^2 a 2^6 clock size CUDA+OpenMPI (one node) | Block size n = (2,4,...,32), for each n, 2^2 to 2^6 clock size CUDA+OpenMPI (two nodes) | Block size n = (2,4,...,64) in two nodes, each one with n/2 processes, for each n, 2^2 to 2^6 block size OpenMPI (two nodes) | Block size n = (2,4,...,32) OpenMPI (two nodes) | Block size n = (2,4,...,64) in two nodes, with n/2 processes each OpenMPI+OpenMP (one node) | Block size n = (2,4,...,32), for each n, 2^2 to 2^6 threads OpenMPI+OpenMP (two nodes) | Block size n = (2,4,...,64) in two nodes, with n/2 processes each and, for each n we have 2^2 to 2^6 threads
Some results
Best Peformance
Worst Peformance
Peformance by varyng the number of threads
Peformance by varyng the number of processes (one node)
Peformance by varyng the number of processes (two nodes)
Peformance by varyng the dimensions of blocks and with 8 processes (Cuda and Cuda+OpenMPI)
Peformance by varyng the dimensions of blocks and with 32 processes (Cuda and Cuda+OpenMPI)
