## Bar Charts: Speedup vs cuBLAS for Matmul Configurations
### Overview
The image contains three bar charts (a, b, c) comparing the speedup of three matrix multiplication (Matmul) implementations—**cuBLAS**, **CUTLASS**, and **LUT_GEMM**—relative to **cuBLAS** across different batch sizes (BS). Each chart corresponds to a specific BS value:
- **a) Matmul BS=1**
- **b) Matmul BS=1024**
- **c) Matmul BS=4096**
The y-axis represents **Speedup vs cuBLAS** (normalized to 1.0 for cuBLAS), and the x-axis lists four configurations: **M0, M1, M2, M3**. The charts use distinct colors for each method:
- **Blue**: cuBLAS
- **Green**: CUTLASS
- **Red**: LUT_GEMM
A dashed horizontal line at **1.0** indicates the baseline (cuBLAS performance).
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### Components/Axes
- **X-axis (Categories)**:
- **M0, M1, M2, M3** (configurations).
- **Y-axis (Values)**:
- **Speedup vs cuBLAS** (0.0 to 5.0 for chart a), 0.0 to 1.25 for charts b and c).
- **Legends**:
- **cuBLAS** (blue bars)
- **CUTLASS** (green bars)
- **LUT_GEMM** (red bars)
- **Annotations**:
- "LUT-GEMM N/A" in red text (indicating missing data for LUT_GEMM in some cases).
- Dashed line at **1.0** (baseline).
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### Detailed Analysis
#### Chart a) Matmul BS=1
- **cuBLAS**:
- M0: ~3.5 (3.4–3.6)
- M1: ~4.0 (3.9–4.1)
- M2: ~3.8 (3.7–3.9)
- M3: ~0.5 (0.4–0.6)
- **CUTLASS**:
- M0: ~2.0 (1.9–2.1)
- M1: ~2.5 (2.4–2.6)
- M2: ~2.3 (2.2–2.4)
- M3: ~0.5 (0.4–0.6)
- **LUT_GEMM**:
- M0: ~1.0 (0.9–1.1)
- M1: ~2.5 (2.4–2.6)
- M2: ~3.0 (2.9–3.1)
- M3: **N/A** (marked in red).
#### Chart b) Matmul BS=1024
- **cuBLAS**:
- M0: ~0.75 (0.73–0.77)
- M1: ~0.70 (0.68–0.72)
- M2: ~0.65 (0.63–0.67)
- M3: ~0.75 (0.73–0.77)
- **CUTLASS**:
- M0: ~0.70 (0.68–0.72)
- M1: ~0.65 (0.63–0.67)
- M2: ~0.60 (0.58–0.62)
- M3: ~0.70 (0.68–0.72)
- **LUT_GEMM**:
- M0: **N/A**
- M1: **N/A**
- M2: **N/A**
- M3: **N/A**
#### Chart c) Matmul BS=4096
- **cuBLAS**:
- M0: ~0.50 (0.48–0.52)
- M1: ~0.45 (0.43–0.47)
- M2: ~0.40 (0.38–0.42)
- M3: ~0.20 (0.18–0.22)
- **CUTLASS**:
- M0: ~0.50 (0.48–0.52)
- M1: ~0.45 (0.43–0.47)
- M2: ~0.40 (0.38–0.42)
- M3: ~0.20 (0.18–0.22)
- **LUT_GEMM**:
- M0: **N/A**
- M1: **N/A**
- M2: **N/A**
- M3: **N/A**
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### Key Observations
1. **cuBLAS Dominates at Low BS (BS=1)**:
- cuBLAS achieves the highest speedup (up to ~4.0) for M1, while CUTLASS and LUT_GEMM show significantly lower performance.
- LUT_GEMM underperforms but matches cuBLAS at M3 (BS=1).
2. **Performance Degradation at Higher BS**:
- For BS=1024 and BS=4096, all methods show speedup values **below 1.0**, indicating **slower performance than cuBLAS**.
- LUT_GEMM is **not applicable (N/A)** for all configurations at BS=1024 and BS=4096, suggesting it may not be optimized for large batch sizes.
3. **Consistent Trends Across Configurations**:
- cuBLAS and CUTLASS exhibit similar trends, with speedup decreasing as BS increases.
- LUT_GEMM’s N/A values imply it is either untested or incompatible with these configurations.
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### Interpretation
- **cuBLAS as Baseline**: The dashed line at 1.0 confirms cuBLAS is the reference for speedup.
- **CUTLASS vs. cuBLAS**: CUTLASS generally matches or slightly underperforms cuBLAS, suggesting it is a competitive alternative but not superior.
- **LUT_GEMM Limitations**: The absence of data for LUT_GEMM at higher BS values (1024, 4096) indicates it may not scale well or is not implemented for these cases.
- **BS Impact**: Speedup decreases with increasing BS, highlighting potential inefficiencies in handling large batch sizes.
This data suggests that **cuBLAS remains the most efficient implementation** for the tested configurations, while **CUTLASS** offers comparable performance. **LUT_GEMM** appears limited in applicability, particularly for large batch sizes.
