Principle:Bitsandbytes foundation Bitsandbytes Matmul Performance Estimation
| Knowledge Sources | |
|---|---|
| Domains | Performance_Modeling, Autotuning, GPU_Optimization |
| Last Updated | 2026-02-07 13:31 GMT |
Overview
An analytical GPU kernel performance model that estimates matrix multiplication execution time by modeling compute throughput, memory bandwidth, and cache behavior to prune autotuning search spaces.
Description
GPU matrix multiplication performance depends on the interaction between compute throughput (tensor cores), memory bandwidth (DRAM and L2 cache), and kernel occupancy. This principle models these three factors analytically to estimate kernel execution time without benchmarking. The total time is modeled as max(compute_time, load_time) + store_time, reflecting the pipelined nature of GPU execution. This estimate enables pruning of Triton autotuning configurations, reducing the number of configurations that need actual benchmarking from potentially hundreds to a handful of promising candidates.
Usage
Apply this principle when autotuning GPU kernels where the search space is large and benchmarking each configuration is expensive. The analytical model filters out clearly suboptimal configurations (those exceeding shared memory, having poor occupancy, or suboptimal pipeline depth).
Theoretical Basis
Where:
Failed to parse (syntax error): {\displaystyle T_{\text{load}} = \frac{\text{DRAM\_bytes}}{\text{DRAM\_BW}} + \frac{\text{L2\_bytes}}{\text{L2\_BW}} }
The model assumes 80% L2 cache hit rate for reused tiles and adjusts bandwidth by CTA occupancy ratio.
Pipeline stage pruning for Ampere+ uses:
# Optimal stages based on MMA-to-ldgsts latency ratio
mma_cycles = (BLOCK_M * BLOCK_N * BLOCK_K) / (16 * 8 * 16) / min(4, num_warps) * 8
optimal_stages = ldgsts_latency / mma_cycles