Performance Analysis

This document presents the benchmarking methodology, performance results, and optimization analysis for TensorCraft-HPC.

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Benchmarking Methodology

Environment

Component	Specification
GPU	NVIDIA A100 80GB
CUDA	12.4
Driver	550.x
OS	Ubuntu 22.04
Compiler	GCC 11.4 / NVCC 12.4

Measurement Protocol

1. Warm-up: 10 iterations before measurement
2. Samples: 100 iterations per measurement
3. Metrics: Mean, standard deviation, min, max
4. Validation: Numerical correctness verified against reference

Baseline References

Operation	Reference Library
GEMM	cuBLAS
Attention	cuDNN / FlashAttention
Normalization	cuDNN
Convolution	cuDNN
Sparse	cuSPARSE

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How to read the numbers

These benchmark tables are meant to answer two different questions:

1. Is the implementation technically serious? Relative performance against NVIDIA libraries is a proxy for whether the kernel structure is sensible.
2. Is the project still educational? TensorCraft-HPC does not aim to disappear behind template metaprogramming or auto-tuned complexity. Some headroom is intentionally traded for readability and explainability.

That means the most important signal is not any single percentage in isolation. The stronger signal is whether the optimization path is coherent, whether the implementation can be reasoned about, and whether the evidence is framed honestly.

Benchmark caveats

• These results should be treated as representative measurements, not universally guaranteed numbers across every GPU and toolchain.
• GitHub-hosted CI runners do not provide CUDA devices, so benchmark reproduction belongs on local GPU-enabled machines.
• Pages and README should present benchmark claims together with methodology and caveats, not as isolated marketing numbers.

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GEMM Performance

FP16 Tensor Core (A100)

Matrix Size	TensorCraft	cuBLAS	Ratio
512×512	0.15ms	0.14ms	93%
1024×1024	0.82ms	0.71ms	87%
2048×2048	3.1ms	2.8ms	89%
4096×4096	12.1ms	11.0ms	91%
8192×8192	95.2ms	88.0ms	92%

Scaling Across Architectures

GPU	SM	4096² FP16	cuBLAS	Ratio
V100	70	14.2ms	12.8ms	89%
A100	80	12.1ms	11.0ms	91%
H100	90	8.5ms	7.8ms	92%

Optimization Stage Analysis

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FlashAttention Performance

Memory Footprint Comparison

Sequence Length	Standard Attention	FlashAttention	Reduction
1024	512 MB	64 MB	8×
2048	2 GB	128 MB	16×
4096	8 GB	256 MB	32×
8192	32 GB	512 MB	64×

Latency Comparison

Config	TensorCraft	cuDNN	Ratio
32×128×64	0.12ms	0.10ms	85%
64×256×64	0.45ms	0.38ms	84%
128×512×64	1.8ms	1.5ms	83%

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Normalization Performance

Operation	TensorCraft	cuDNN	Ratio
LayerNorm (4096×4096)	0.08ms	0.07ms	95%
RMSNorm (4096×4096)	0.06ms	0.05ms	95%
Fused LayerNorm + Dropout	0.09ms	0.08ms	94%

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Convolution Performance

Config	TensorCraft	cuDNN	Ratio
Conv2D 3×3, 256×256	0.42ms	0.35ms	78%
Conv2D 1×1, 512×512	0.28ms	0.22ms	78%
Depthwise 3×3	0.15ms	0.12ms	80%

Performance Gap

Convolution kernels use Im2Col optimization. Further gains require Winograd algorithm and auto-tuning, which are planned for future releases.

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Sparse Operations Performance

Operation	Format	TensorCraft	cuSPARSE	Ratio
SpMV	CSR	0.35ms	0.30ms	88%
SpMM	CSR	1.2ms	1.0ms	85%

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Performance Model

Roofline Analysis

◆TheoremRoofline Bound

For a compute kernel with arithmetic intensity I (FLOP/byte), achieved performance P is bounded by the minimum of memory bandwidth and peak compute:

$P \le \min\left(I \cdot \text{BW}_{\text{mem}},\; \text{TP}_{\text{peak}}\right)$

The transition between memory-bound and compute-bound regimes occurs at the roofline ridge point:

$I_{\text{ridge}} = \frac{\text{TP}_{\text{peak}}}{\text{BW}_{\text{mem}}}$

The performance of GEMM is bounded by:

1. Memory Bandwidth: For small matrices (I < I_ridge)
2. Compute Throughput: For large matrices (I ≥ I_ridge)

The critical matrix size where regime transitions occurs at:

M_critical = (Memory_BW) / (Compute_TP / sizeof(T))

For A100 with FP16:

• Memory BW: 2039 GB/s
• Tensor Core TP: 312 TFLOPS
• M_critical ≈ 256

Arithmetic Intensity

Operation	Arithmetic Intensity	Bound
GEMM	O(N)	Compute
FlashAttention	O(N)	Compute
LayerNorm	O(1)	Memory
Softmax	O(1)	Memory

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Optimization Techniques

Memory Coalescing

// Bad: Strided access
float val = input[threadIdx.x * stride];

// Good: Coalesced access
float val = input[threadIdx.x];

Shared Memory Banking

// Avoid bank conflicts
__shared__ float tile[32][33];  // +1 for padding
tile[ty][tx] = ...;  // No bank conflicts

Warp-Level Primitives

// Efficient reduction within warp
float sum = warp_reduce_sum(val);

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Benchmark Reproduction

# Build benchmarks
cmake --preset release
cmake --build --preset release --parallel 2

# Run GEMM benchmark
./build/release/benchmarks/gemm_benchmark --benchmark_filter="FP16"

# Run all benchmarks
ctest --preset release -R benchmark

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Benchmark regression policy

TensorCraft-HPC currently treats performance regression review as a local GPU-machine discipline, not a hosted-CI guarantee.

This is intentional:

• the repository validates CPU smoke builds, packaging, and Pages automatically
• benchmark binaries require CUDA-enabled machines
• performance claims should be reviewed alongside profiler traces and methodology, not reduced to a green/red hosted workflow badge

For serious regression checks, use one controlled machine, one fixed driver/toolkit stack, and keep the comparison against the same reference library version.

What strong results look like

Signal	Why it matters
Stable relative ratios across nearby input sizes	Suggests the kernel structure is coherent, not overfit to one benchmark
Clear profiler explanation for gaps	Shows engineering judgment rather than cargo-cult optimization
Honest caveats around unsupported cases	Increases trust more than inflated headline numbers
Consistency between code, docs, and benchmark commands	Makes the project easier to evaluate in interviews and code review