Numc

Project Overview

Numc is a high-performance matrix multiplication library written in C with Python bindings. It provides optimized implementations of common matrix operations, with a focus on speed and efficiency. The library achieves significant performance improvements over naive implementations and is competitive with industry-standard libraries like NumPy for certain operations.

Key Features

Numc implements the following core features:

• Matrix Operations: Fast implementations of addition, multiplication, power, and negation
• Python Integration: Seamless Python bindings for easy use in data science workflows
• Memory Efficiency: Optimized memory usage for large matrix operations
• Multi-threading: Parallel execution for improved performance on multi-core systems
• SIMD Vectorization: Utilizes CPU vector instructions for additional speedup

Technical Implementation

Numc employs several optimization techniques to achieve its performance:

• Cache Optimization: Block-based algorithms to maximize cache utilization
• Loop Unrolling: Reduces loop overhead and enables better instruction pipelining
• SIMD Instructions: Uses AVX/SSE instructions for parallel data processing
• OpenMP: Implements multi-threading for parallel execution across CPU cores
• Memory Alignment: Ensures data is properly aligned for optimal memory access
• Python C API: Efficient integration with Python using the C extension API

Performance Results

Benchmark results show significant performance improvements:

• Matrix multiplication: Up to 60x faster than naive Python implementation
• Matrix power operations: Up to 80x speedup over baseline
• Comparable performance to NumPy for many operations, with superior performance for specific matrix sizes
• Near-linear scaling with additional CPU cores for large matrices

Code Example

Using Numc in Python is straightforward:

import numc as nc # Create matrices a = nc.Matrix(3, 3, [1, 2, 3, 4, 5, 6, 7, 8, 9]) b = nc.Matrix(3, 3, [9, 8, 7, 6, 5, 4, 3, 2, 1]) # Perform operations c = a * b # Matrix multiplication d = a + b # Matrix addition e = a ** 2 # Matrix power f = -a # Matrix negation print(c)

Implementation Challenges

Developing Numc presented several interesting challenges:

• Balancing code readability with performance optimizations
• Determining optimal block sizes for different matrix dimensions
• Managing memory allocation and deallocation efficiently
• Handling edge cases for unusual matrix shapes
• Debugging parallel code with race conditions
• Creating a clean Python API that feels natural to users

Future Enhancements

Planned improvements to Numc include:

• GPU acceleration using CUDA or OpenCL
• Support for sparse matrices
• Additional matrix decomposition algorithms
• Improved error handling and diagnostics
• Expanded test suite for edge cases