This module covers essential parallel algorithm patterns that form the building blocks of high-performance GPU computing, including convolution, stencil computations, histogram operations, reduction patterns, and prefix sum algorithms.
By completing this module, you will:
- Master convolution algorithms for 1D, 2D, and 3D data with separable filter optimizations
- Implement efficient stencil computations with halo region management and boundary conditions
- Design histogram algorithms using atomic operations, privatization, and coarsening techniques
- Optimize reduction patterns with tree reductions, segmented approaches, and multi-level strategies
- Apply prefix sum algorithms for inclusive/exclusive scan, segmented scan, and large array processing
- Analyze algorithmic complexity and performance trade-offs between different approaches
- Develop cross-platform implementations supporting both NVIDIA CUDA and AMD ROCm
Recommended Requirements:
- CUDA Toolkit 12.0+ or ROCm 6.0+
- content.md - Comprehensive guide covering all fundamental parallel algorithm patterns
Comprehensive convolution implementations for various dimensionalities:
- 1D Convolution: Signal processing, digital filters, time-series analysis
- 2D Convolution: Image processing, computer vision kernels
- 3D Convolution: Volumetric data processing, medical imaging
- Separable Convolution: Optimization technique for separable filters
- FFT-based Convolution: Large kernel optimization using Fast Fourier Transform
Key Concepts:
- Halo region loading and boundary condition handling
- Shared memory tiling for performance optimization
- Separable filter decomposition for computational efficiency
- Memory coalescing in convolution patterns
- Cross-platform optimization for different GPU architectures
Performance Characteristics:
- Naive convolution: O(N * M) where N is data size, M is kernel size
- Separable convolution: O(N * √M) for square kernels
- FFT convolution: O(N log N) for large kernels
Finite difference methods and stencil-based computations:
- 1D Stencil: Heat equation, wave propagation simulation
- 2D Stencil: Laplacian operator, image processing filters
- 3D Stencil: Computational fluid dynamics, physics simulations
- Variable Stencil: Adaptive stencil patterns
- Multi-stage Stencil: Temporal blocking and optimization
Key Concepts:
- Ghost cell management and periodic boundaries
- Temporal blocking for cache optimization
- Thread coarsening for improved performance
- Register tiling techniques
- NUMA-aware memory access patterns
Optimization Strategies:
- Shared memory blocking to reduce global memory accesses
- Thread coarsening to improve arithmetic intensity
- Register blocking for temporal locality
- Overlapping computation with communication
Atomic operations and histogram construction techniques:
- Basic Histogram: Atomic increment operations
- Privatized Histogram: Per-block private histograms
- Coarsened Histogram: Thread coarsening for reduced contention
- Aggregated Histogram: Warp-level aggregation techniques
- Multi-pass Histogram: Large dataset handling
Key Concepts:
- Atomic operation optimization and contention reduction
- Privatization strategies for improved performance
- Coarsening techniques to reduce atomic pressure
- Warp-level aggregation using shuffle operations
- Load balancing for irregular data distributions
Performance Analysis:
- Atomic contention effects on performance
- Privatization vs. global atomic trade-offs
- Memory bandwidth vs. compute utilization
- Scaling behavior with input size and distribution
Comprehensive reduction algorithm implementations:
- Tree Reduction: Classical parallel reduction tree
- Segmented Reduction: Multiple independent reductions
- Multi-level Reduction: Hierarchical reduction for large datasets
- Warp-level Reduction: Modern CUDA cooperative groups
- Custom Reduction: Application-specific reduction operations
Key Concepts:
- Work vs. depth complexity trade-offs
- Thread divergence minimization techniques
- Bank conflict avoidance in shared memory
- Warp-level primitives and shuffle operations
- Load balancing across processing elements
Algorithm Variants:
- Hillis-Steele: O(n log n) work, O(log n) depth
- Brent-Kung: O(n) work, O(log n) depth
- Segmented reduction for multiple sequences
- Hierarchical approaches for very large datasets
Scan operations for parallel prefix computations:
- Inclusive Scan: Forward cumulative operations
- Exclusive Scan: Shifted cumulative operations
- Segmented Scan: Independent scans within segments
- Large Array Scan: Multi-pass techniques for arbitrary sizes
- Custom Scan Operations: Beyond simple addition
Key Concepts:
- Up-sweep and down-sweep phases
- Work-efficient vs. step-efficient algorithms
- Multi-level scanning for large arrays
- Segmentation for independent subsequences
- Custom associative operations
Applications:
- Compact operations and stream compaction
- Radix sort digit processing
- Parallel resource allocation
- Dynamic load balancing
- Graph algorithm building blocks
Platform-specific optimizations and portability:
- NVIDIA-specific Optimizations: Warp-level primitives, cooperative groups
- AMD-specific Optimizations: Wavefront operations, LDS optimization
- Portable Implementations: HIP code working on both platforms
- Performance Comparison: Benchmarking across architectures
- Architecture Detection: Runtime adaptation to hardware capabilities
Key Concepts:
- Warp (32 threads) vs. Wavefront (64 threads) considerations
- Shared memory vs. Local Data Store (LDS) optimization
- Platform-specific intrinsics and primitives
- Performance portability strategies
- Runtime hardware capability detection
# Check GPU configuration
nvidia-smi && nvcc --version # NVIDIA setup
rocm-smi && hipcc --version # AMD setup
# Verify compute capabilities
make system_infoMinimum Requirements:
- CUDA Toolkit 11.0+ or ROCm 5.0+
- Compute Capability 6.0+ recommended
- 8GB+ GPU memory for large dataset examples
- C++14 compatible compiler
# Build all examples
make all
# Build CUDA examples only
make cuda
# Build ROCm/HIP examples only
make rocm
# Build specific algorithm category
make convolution # Convolution algorithms
make stencil # Stencil computations
make histogram # Histogram operations
make reduction # Reduction patterns
make prefix_sum # Prefix sum algorithms
make cross_platform # Cross-platform examples# Comprehensive algorithm testing
make test
# Performance benchmarking
make benchmark
# Algorithm correctness validation
make validate
# Cross-platform comparison
make compare_platforms
# Individual algorithm testing
make test_convolution
make test_stencil
make test_histogram
make test_reduction
make test_prefix_sum| Algorithm | Work Complexity | Depth Complexity | Memory Usage | Best Use Case |
|---|---|---|---|---|
| 1D Convolution | O(N * M) | O(1) | O(N + M) | Signal processing |
| 2D Convolution | O(N² * M²) | O(1) | O(N² + M²) | Image processing |
| Separable Convolution | O(N² * M) | O(1) | O(N² + M) | Large kernel optimization |
| Tree Reduction | O(N) | O(log N) | O(N) | Parallel aggregation |
| Prefix Sum (Hillis-Steele) | O(N log N) | O(log N) | O(N) | Simple implementation |
| Prefix Sum (Brent-Kung) | O(N) | O(log N) | O(N) | Work-efficient scan |
| Histogram (Atomic) | O(N) | O(1) | O(B) | Sparse distributions |
| Histogram (Privatized) | O(N) | O(log P) | O(B * P) | Dense distributions |
# Run comprehensive performance analysis
make performance_analysis
# Generate performance reports
make performance_report
# Compare algorithm variants
make algorithm_comparison
# Profile with vendor tools
make profile_nvidia # Nsight Compute profiling
make profile_amd # ROCProfiler analysis-
Memory Access Optimization:
- Coalesced global memory access patterns
- Shared memory tiling and blocking
- Register blocking for temporal locality
- Cache-aware algorithm design
-
Computational Optimization:
- Thread coarsening and loop unrolling
- Warp-level primitive utilization
- Instruction-level parallelism
- Algorithmic complexity reduction
-
Load Balancing:
- Work stealing for irregular computations
- Dynamic load distribution
- Adaptive granularity control
- NUMA-aware scheduling
NVIDIA CUDA Optimizations:
- Warp-level collective operations
- Cooperative groups programming model
- Tensor Core utilization for applicable algorithms
- NVLINK optimization for multi-GPU
AMD ROCm Optimizations:
- Wavefront-level operations (64 threads)
- Local Data Store (LDS) optimization
- GCN/RDNA architecture considerations
- Infinity Fabric optimization
HIP Portability:
- Single source code for both platforms
- Runtime architecture detection
- Performance-portable implementations
- Platform-specific optimization paths
- Computational Fluid Dynamics: Stencil computations for finite difference methods
- Image Processing: Convolution operations for computer vision
- Signal Processing: 1D convolution for digital signal processing
- Monte Carlo Simulations: Reduction operations for statistical analysis
- Convolutional Neural Networks: Optimized convolution implementations
- Batch Processing: Efficient reduction and aggregation operations
- Data Preprocessing: Histogram analysis and normalization
- Feature Extraction: Prefix sum for compact operations
- Stream Processing: Online algorithm implementations
- Database Operations: Parallel aggregation and sorting primitives
- Compression Algorithms: Prefix sum for encoding/decoding
- Graph Analytics: Reduction patterns for graph algorithms
-
Memory-Related Problems:
- Insufficient GPU memory for large datasets
- Bank conflicts in shared memory access
- Uncoalesced global memory patterns
- Cache thrashing in large array processing
-
Performance Issues:
- Atomic contention in histogram operations
- Thread divergence in reduction trees
- Load imbalance in irregular computations
- Insufficient occupancy due to resource usage
-
Algorithmic Issues:
- Numerical precision in iterative algorithms
- Boundary condition handling in stencil operations
- Overflow in prefix sum operations
- Correctness in segmented operations
# Memory debugging
cuda-memcheck ./example # NVIDIA memory checking
rocm-debug-agent ./example # AMD memory debugging
# Performance analysis
ncu --metrics all ./example # NVIDIA detailed profiling
rocprof --stats --hip-trace ./example # AMD performance analysis
# Correctness validation
make debug # Debug builds with assertions
make validate_all # Comprehensive correctness testingModule 6 provides comprehensive coverage of fundamental parallel algorithms essential for high-performance GPU computing:
- Algorithmic Foundations: Master the building blocks of parallel computation
- Performance Optimization: Apply advanced optimization techniques across algorithms
- Cross-Platform Development: Create portable high-performance implementations
- Real-World Applications: Connect algorithmic concepts to practical applications
These algorithms form the foundation for more complex applications covered in subsequent modules and are essential for building efficient GPU-accelerated software.
Duration: 8-10 hours
Difficulty: Intermediate-Advanced
Prerequisites: Modules 1-5 completion, parallel algorithm concepts
Note: This module emphasizes both educational understanding and optimized implementations. Focus on mastering the algorithmic concepts before diving into platform-specific optimizations.