hpc benchmark hpl hpcg

**HPC Benchmarking (HPL/HPCG)** establishes **standardized performance measurements for supercomputers, enabling fair comparison across architectures and identifying achievable sustained performance on realistic workloads.** **High Performance LINPACK (HPL) Benchmark** - **HPL Algorithm**: Dense LU factorization with partial pivoting (Ax = b solution). Highly optimized, cache-friendly operation; achieves 80-90% theoretical peak on modern hardware. - **Matrix Size**: Adjustable N (problem dimension). Typical: N = 100,000-5,000,000 (depends on available memory). Larger N better utilizes memory bandwidth. - **Computation**: O(2N³/3) floating-point operations. Perfect for profiling (predictable load, uniform memory access). - **Measurement**: GFLOP/s = (2N³/3) / wall-clock time. Top500 list ranked by HPL performance. **HPL Scaling Characteristics** - **Weak Scaling**: Fixed work per processor. Increase processors + matrix size proportionally. Time = constant (ideal). HPL scales to 100,000+ cores. - **Strong Scaling**: Fixed problem size. Increase processors, time decreases. Eventually communication dominates; speedup saturates. - **Efficiency**: Sustained GFLOP/s / Theoretical peak GFLOP/s. Modern systems achieve 80-90% HPL efficiency (vs 10-30% for irregular applications). - **Tuning**: Matrix size, process grid (P×Q), block size (NB) all impact performance. Tuned HPL achieves near-peak throughput. **HPCG (High-Performance Conjugate Gradient) Benchmark** - **HPCG Algorithm**: Sparse symmetric positive-definite system solved via CG with multigrid preconditioning. Memory-bound, irregular access patterns. - **Advantages Over HPL**: HPL unrealistic (dense linear algebra rare in science); HPCG more representative of real applications (structural mechanics, CFD, electromagnetics). - **Sparse Matrix**: 3D stencil (~27-point stencil, only ~27 nonzeros per row). Structured sparsity, but irregular memory access. - **Multigrid Preconditioning**: Coarse grids constructed automatically (AMG). Multiple levels of processing. Memory-bound bottleneck (low arithmetic intensity). **HPCG Metrics** - **Throughput**: GFLOP/s (same as HPL, but lower numbers typical). 10-50 GFLOP/s vs 100+ GFLOP/s HPL on same machine (5-10x difference). - **Memory Bandwidth Efficiency**: HPCG measures memory bandwidth utilization indirectly (embedded in GFLOP/s). Typical: 20-40% of theoretical memory bandwidth. - **Problem Size**: Adjustable N (array dimension). Typical: N = 100-10,000. Smaller than HPL (memory-limited). - **Green500 Ranking**: HPCG combined with power consumption (watts) creates energy efficiency ranking. Energy per GFLOP metric. Leading systems: 20-40 MFLOP/watt. **HPL vs HPCG Comparison** - **HPL Throughput-Oriented**: Peak performance demonstration. Ideal for vendor marketing. Not representative of real workloads. - **HPCG Realism**: More representative of application behavior (memory-bound, sparse). Better predictor of actual application performance on system. - **System Ranking Correlation**: HPL rank differs from HPCG (e.g., systems with large caches rank higher in HPL than HPCG). Reveals architecture trade-offs. - **Procurement Value**: Both benchmarks used by facilities to evaluate systems. HPL important for peak performance marketing; HPCG important for sustained performance. **Top500 List Methodology** - **Ranking Criterion**: Sustained LINPACK performance (HPL GFLOP/s). Updated twice yearly (June, November). - **Threshold**: Entry #500 sets minimum performance (~1 PFLOP/s in 2024). Systems below threshold not ranked. - **Rmax (Achieved Performance)**: Actual HPL performance measured (with tuning allowances). Conservative estimate → likely achievable on comparable systems. - **Rpeak (Theoretical Peak)**: Manufacturer specification × core count × clock rate. Rpeak typically 2-3x Rmax (realistic difference). **Green500 and Alternative Benchmarks** - **Green500**: Separate ranking emphasizing energy efficiency. GFLOP/watt metric. Data center power consumption critical; efficiency rankings increasingly important. - **NAS Parallel Benchmarks**: Application-based benchmarks (CFD, sparse LU, etc.). More realistic than HPL but less standardized. - **Sandia Mantevo**: Proxy applications mimicking real workloads. Smaller scale, shorter runtime than full application. Good for procurement testing. - **Application-Specific Benchmarks**: DL (Resnet, Transformer training), HPC (WRF weather, GROMACS molecular dynamics). Industry-relevant performance metrics. **Benchmark Methodology and Reproducibility** - **HPL Run Rules**: Specific rules for code generation, compiler flags, network tuning. Ensures comparison fairness but allows vendor optimization. - **Reproducibility**: Multiple runs required, statistical significance checked. Variability typically <5% (excellent). - **Tuning Scope**: Compiler optimization, blocking factors, process layout all tunable. Tuning often consumed as part of benchmark time. - **Credibility**: Independent verification (Top500 committee) checks submitted results. Outliers questioned, spot checks performed on suspicious results.