Explain Amdahl’s law and GPU matmul optimization

Answer the following systems/performance fundamentals questions (as in a GPU/ML infra interview). Assume a modern NVIDIA-like GPU architecture unless otherwise stated.

1. Amdahl’s law : What is it, what does it imply about parallel speedup, and how do you use it to reason about optimizations?
2. GPU memory hierarchy : Compare registers , shared memory / SRAM , L1/L2 cache , and HBM/global memory . What are typical latency/bandwidth trade-offs, and what code patterns map well to each level?
3. Threading limits :
   • What is a warp/wavefront ?
   • What limits the maximum number of concurrent threads (per block and per SM), and how do registers/shared-memory usage affect occupancy ?
4. Matrix multiplication (matmul) :
   • What is the time complexity of multiplying an $m\times k$ matrix by a $k\times n$ matrix?
   • How does a tiled GPU implementation work conceptually (what is “tiling/blocking” and why does it help)?
5. CPU vs GPU matmul : Why are high-performance implementations different on CPU vs GPU? Discuss SIMD, cache behavior, memory bandwidth, and parallelism.
6. C++ fundamentals :
   • What is a virtual function , and what runtime cost does it introduce?
   • What does inline mean in C++? When is inlining likely/unsafe/unhelpful?