objblas: Roofline Performance Analysis of AXPY Implementations

This repository contains Fortran implementations and performance analysis of the AXPY operation (y ← αx + y) using different approaches:

• Standard BLAS
• OpenMP parallel
• OpenMP with SIMD
• OpenMP with custom scheduling

Project Structure

• src/ — Fortran source files for BLAS and OpenMP implementations
• test/axpy_perf.f90 — Main performance test program
• test/axpy_perf.f90 — Measures and compares the performance of all AXPY implementations, writing results to results.csv
• results.csv — Output file with measured performance data

How It Works

The test program:

1. Prompts for system memory bandwidth (GB/s), peak GFLOPS, problem size n, and number of repetitions
2. Allocates and initializes vectors x and y
3. Runs each AXPY implementation, measuring execution time
4. Computes:
   • Operational Intensity (OI): $\frac{1}{12}$ FLOPS/Byte (for double precision)
   • Measured GFLOPS for each implementation
   • Theoretical roofline (max achievable GFLOPS): $\min$(Peak GFLOPS, OI × Memory Bandwidth)
   • Percentage of roofline achieved by each implementation
5. Outputs results to the terminal and to results.csv

Roofline Model

• AXPY FLOPs: $2n$ (1 multiply + 1 add per element)
• Data movement: $3n$ (read x, read y, write y)
• Operational Intensity: $\frac{2n}{3n \times 8}$ = $\frac{1}{12}$ FLOPS/Byte
• Memory-bound ceiling: OI × Memory Bandwidth
• Maximum achievable performance: $\min$(Peak GFLOPS, OI × Memory Bandwidth)

Example Output

 Enter memory bandwidth in GB/s: 
89.6
 Enter peak performance in GFLOPS: 
844
 Enter problem size (n): 
100000
 Enter number of repetitions: 
50
 Testing AXPY with n =       100000
 ==================================================
 Roofline Model Analysis
 ==================================================
 System Parameters:
   Peak Performance:    844.00000000000000       GFLOPS
   Memory Bandwidth:    89.599999999999994       GB/s
 
 AXPY Characteristics:
   Operational Intensity:    8.3333333333333329E-002  FLOPS/Byte
   Memory-bound ceiling:    7.4666666666666659       GFLOPS
   Maximum achievable:    7.4666666666666659       GFLOPS
 
 Measured Performance:
  BLAS:                7.133314 GFLOPS,        85.60 GB/s ( 95.54% of max)
  OpenMP:              7.303652 GFLOPS,        87.64 GB/s ( 97.82% of max)
  OpenMP SIMD:         7.221572 GFLOPS,        86.66 GB/s ( 96.72% of max)
  OpenMP Schedule:     7.406552 GFLOPS,        88.88 GB/s ( 99.19% of max)
 ==================================================

Usage

1. Build the project using CMake or your preferred Fortran build system
2. Run the axpy_perf executable
3. Enter the required parameters when prompted
4. Analyze the output in the terminal and in results.csv

Requirements

• Fortran compiler with OpenMP support
• BLAS library
• CMake (for building)

Exercise

You can play around with the implementation in the blasOMP.f90 module to see if you can obtain better measurements for your axpy.