Parallel Pi Approximation with MPI 🧠💻

This project implements a high-performance parallel approximation of π using the midpoint rule and MPI. It was benchmarked on the Bridges2 supercomputer using SLURM with 1, 12, 24, and 48 cores.

📌 Key Features

• ✅ 4 implementations: pi1.cpp through pi4.cpp
• ✅ Uses MPI_Reduce and MPI_Bcast
• ✅ Includes SLURM scripts to run on HPC clusters
• ✅ Full report analyzing performance, speedup, and scaling behavior

🖥️ Technologies Used

• C++
• OpenMPI
• SLURM
• HPC (Bridges2 @ Pittsburgh Supercomputing Center)

📊 Performance Summary

Cores	Time (s)	Speedup	Efficiency (%)
1	3.50	1.00	100.0
12	0.345	10.14	84.5
24	0.346	10.12	42.1
48	3.50	1.00	2.0

📎 Files Included

• pi1.cpp to pi4.cpp: Four stages of parallel implementation
• SLURM job scripts: job-pi2-01.slurm, etc.
• report.txt: Final project report with results and analysis

##folder Structure

parallel-pi-mpi-hpc/
├── src/
│   ├── pi1.cpp
│   ├── pi2.cpp
│   ├── pi3.cpp
│   └── pi4.cpp
├── jobs/
│   ├── job-pi2-01.slurm
│   ├── job-pi2-12.slurm
│   ├── job-pi2-24.slurm
│   └── job-pi2-48.slurm
├── results/
│   └── timing-analysis.csv    ← (optional)
├── report.txt
├── README.md
└── LICENSE

📘 What I Learned

• Writing MPI programs in C++
• Measuring parallel performance and speedup
• SLURM job submission and HPC benchmarking
• Communication overhead and scalability limits

📌 Author

Jesús Gil
M.S. Computer Science
LinkedIn • GitHub