arithmetic intensity

**Arithmetic intensity** is the **ratio of floating-point operations to bytes moved from memory** - it indicates whether workload performance is likely limited by compute capacity or memory bandwidth. **What Is Arithmetic intensity?** - **Definition**: FLOPs per byte metric used in roofline-style performance analysis. - **Interpretation**: Low intensity suggests memory-bound behavior, while high intensity tends toward compute-bound. - **Workload Examples**: Elementwise transforms are often low intensity, dense GEMM is typically high intensity. - **Optimization Link**: Fusion and tiling can increase intensity by improving data reuse. **Why Arithmetic intensity Matters** - **Bottleneck Prediction**: Intensity quickly signals which hardware limit dominates runtime. - **Kernel Design**: Guides whether to prioritize memory-access optimization or arithmetic throughput. - **Performance Modeling**: Enables roofline comparisons against theoretical hardware ceilings. - **Resource Planning**: Helps match workloads to hardware classes with appropriate bandwidth or compute ratio. - **Optimization Prioritization**: Avoids wasted effort on compute tuning when memory movement is the real constraint. **How It Is Used in Practice** - **Metric Estimation**: Compute approximate FLOPs and byte traffic for major kernels. - **Roofline Placement**: Plot kernels on roofline to identify memory- or compute-bound regions. - **Improvement Actions**: Increase data reuse and fuse operations to shift low-intensity kernels upward. Arithmetic intensity is **a powerful diagnostic metric for performance strategy** - understanding work-per-byte ratio is essential for choosing the right optimization path.