Understanding Application Performance with Roofline Modeling

with calculating an software’s efficiency is that the real-world efficiency and theoretical efficiency can differ. With an ecosystem of merchandise that’s rising with excessive efficiency wants comparable to Excessive Efficiency Computing (HPC), gaming, or within the present panorama – Giant Language Fashions (LLMs), it’s important to calculate precisely the efficiency of an software.

Merely measuring theoretical GFLOPs (Floating-Level Operations Per Second) shouldn’t be sufficient, as purposes not often attain these maximums in the actual world. That is the place the Roofline Mannequin is available in, providing a transparent visible methodology to estimate an software’s efficiency and highlighting the crucial position of hardware-specific optimizations.

Why easy metrics aren’t sufficient

Once we take into consideration measuring efficiency, there are a couple of metrics that come to thoughts:

• Execution time: This tells you how lengthy a process took however gives no perception into why.
• Cycles per Directions (CPI): This only measures the processor’s compute efficiency.
• Serial vs Parallel execution: Measures compute efficiency overlooking any {hardware} optimizations.
• Floating Level Operations Per Second (FLOP/s): This only represents a theoretical most which is usually not achievable in a real-world state of affairs.

Whereas these are good metrics, they typically don’t present sufficient info. For example, utilizing the Floating Level Operations Per Seconds is a theoretical restrict which isn’t typically achieved. So utilizing that because the solely metric shouldn’t be sufficient because it ignores a standard efficiency limiter – information motion.

Roofline Modeling

The Roofline Mannequin is a strong software that visually maps an software’s efficiency towards the capabilities of a selected {hardware} structure, comparable to a CPU or GPU. The mannequin will get its title from the form of the graph it produces, which incorporates a “roof” composed of a slanted line and a flat, horizontal line. This form represents the last word efficiency limits imposed by the {hardware}.

From this modeling method, there are two parameters which outline the achievable limits with {hardware}:

• Information motion: The time it takes to maneuver information, calculated as the full information measurement divided by the system’s peak reminiscence bandwidth.
• Computation: The time required for calculations, decided by dividing the full variety of floating-point operations by the system’s peak compute efficiency (generally measured in GFLOP/s).

The entire execution time of an software is decided by the better of those two values: max {data_movement, computation}.

Regardless of the {hardware} having higher compute efficiency, information motion can typically develop into the bottleneck. Roofline Modeling introduces the idea of Arithmetic Depth (AI). AI is the ratio of floating-point operations carried out for each byte of knowledge moved from reminiscence.

• An algorithm with excessive Arithmetic Depth is taken into account compute-hungry. Its efficiency is restricted by how rapidly calculations may be carried out.
• An algorithm with low Arithmetic Depth is taken into account data-hungry. Its efficiency is restricted by how rapidly information may be moved.

Understanding the graph

A Roofline graph plots the Attainable FLOP/s (y-axis) towards the Arithmetic Depth (x-axis). The “roof” itself reveals the {hardware}’s limitations. The slanted a part of the roof represents the height information bandwidth (in GB/s), whereas the flat half represents the height computational efficiency (in GFLOPS). Word that every thing within the picture is in a logarithmic scale.

• Factors beneath the roof: Point out suboptimal efficiency indicating scope of enchancment.
• Factors hitting the slanted line: Information hungry software. Its efficiency is restricted by information bandwidth.
• Factors hitting the flat line: Compute hungry software. It’s utilizing the complete computational energy of the processor.

Why is Roofline Modeling essential?

Roofline Modeling supplies a visible, intuitive strategy to perceive software efficiency, displaying key traits like Operational Depth, GPU capabilities, and attainable FLOP/s. This sort of modeling helps the programmer make focused optimizations to their software for {hardware} with which higher outcomes may be obtained.

• Bottleneck evaluation: Having a visible support makes it simple for the developer to determine the place the bottleneck is – reminiscence or efficiency. If the appliance is reminiscence intensive, a developer can deal with enhancing information locality with methods like caching or loop tiling. If it’s compute intensive, the main focus can shift to enabling extra parallel computations or leveraging compiler optimizations.
• {Hardware} and software program design: Software program engineers shouldn’t concern the underlying {hardware}. As a substitute, the {hardware} design must be embraced and optimized. Software program engineers can use insights from Roofline Modeling to embrace and optimize for the particular structure they’re utilizing.

Roofline Modeling in Motion

To carry out Roofline Modeling, we have to profile the appliance to know the efficiency. From profiling, we will get metrics comparable to Floating Level Operations (FLOPs) and reminiscence bandwidth utilization, each of that are required for Roofline Modeling. This text explores two of those instruments – Nvidia’s ncu which is the Nsight Compute CLI for GPU evaluation and PyTorch’s profiler, particularly for purposes utilizing PyTorch.

For detailed CUDA kernel optimization and exact FLOP/byte calculations, ncu supplies direct GPU {hardware} counter info. In distinction, torch.profiler.profile gives a higher-level perspective inside PyTorch, serving to within the understanding of operator-level efficiency, tensor reminiscence utilization, and the general software habits encompassing each CPU and GPU actions.

Profiling with ncu

ncu is the command line interface which is used for profiling CUDA kernels [2]. It could actually show outcomes straight within the terminal or save them to a log file for later evaluation. To construct a Roofline mannequin, we have to seize the particular metrics that can permit us to calculate Arithmetic Depth.

We’ll use the PyTorch ImageNet repository [3] as our instance. It’s a good selection as a result of it’s simple to know, well-documented by PyTorch, and works with their profiler, so we will actually dig into the efficiency.

Step 1: Run the ncu command to gather metrics

Step one is to run the appliance by means of ncu to gather the required hardware-level information. The command appears to be like like this:

ncu --log-file  
    --metrics  
    --target-processes all 
    python3 

• log-file: The log file during which we wish to retailer the outcomes.
• metrics: That is an important parameter and depicts the metrics that we wish to seize. For calculating Arithmetic Depth, we contemplate:
  • dram__sectors_write.sum : sum of DRAM sectors written
  • dram__sectors_read.sum : sum of DRAM sectors learn
  • smsp__sass_thread_inst_executed_op_fadd_pred_on.sum : sum of floating-point additions
  • smsp__sass_thread_inst_executed_op_fmul_pred_on.sum : sum of floating-point multiplications
  • smsp__sass_thread_inst_executed_op_ffma_pred_on.sum : sum of floating-point fused multiply add operations
• target-process: all flag ensures that we profile your entire software.

Our ncu command modifications to:

ncu --log-file logs_example --metrics dram__sectors_write.sum, 
dram__sectors_read.sum, 
smsp__sass_thread_inst_executed_op_fadd_pred_on.sum,  
smsp__sass_thread_inst_executed_op_fmul_pred_on.sum, 
smsp__sass_thread_inst_executed_op_ffma_pred_on.sum 
--target-processes all python3 
primary.py /imagenet --arch resnet50 --epochs 1 --batch-size 10 
--print-freq 10 --seed 42

Step 2: Calculating FLOPs from the metrics

As soon as the profiler has run, we will combination the collected metrics to calculate the full floating-point operations. The formulation is:

[FLOPs = 2 * FMA_count + FADD_count + FMUL_count]

• FLOPs: Depend of Floating Level Operations.
• FMA_count: Fused Multiply-Add (FMA) operations usually rely as 2 FLOPs (one multiplication and one addition). That is represented by the smsp__sass_thread_inst_executed_op_ffma_pred_on.sum metric.
• FADD_count: That is represented by the smsp__sass_thread_inst_executed_op_fadd_pred_on.sum metric.
• FMUL_count: That is represented by the smsp__sass_thread_inst_executed_op_fmul_pred_on.sum metric.

Step 3: Calculate the bytes transferred

Subsequent, we calculate the full information transferred to and from DRAM. The ncu metrics present the variety of DRAM sectors learn and written. Assuming a standard sector measurement of 32 bytes for contemporary GPUs:

[Total_DRAM_bytes = (dram__sectors_read.sum + dram__sectors_write.sum) * 32]

Step 4: Calculate the Arithmetic Depth

With FLOPs and whole bytes, we will now calculate the Arithmetic Depth:

[AI = FLOPs / Total_DRAM_Bytes]

Step 5: Calculate execution time

To search out the appliance’s efficiency in FLOP/s, we additionally want the execution time. For this, we will use NVIDIA Nsight Techniques (nsys), a system-wide profiler that may precisely measure the runtime of software segments. We run our software once more, this time with nsys, to generate a time-based report. From this report, we will extract the full GPU operating time.

nsys profile -f true -o  python3 

Our nsys command modifications to:

nsys profile -f true -o time.qdrep python3 primary.py /imagenet 
--arch resnet50 --epochs 1 --batch-size 10 --print-freq 10 
--seed 42

After operating this command, we will get the GPU_RUNNING_TIME.

Step 6: Calculate the appliance efficiency

Lastly, we calculate the achieved efficiency in FLOP/s by dividing the full FLOPs by the execution time:

[FLOP/s = FLOPs / GPU_RUNNING_TIME]

This worth provides us the “attainable FLOP/s” that we will plot on our Roofline graph.

Profiling with torch

For purposes written in PyTorch, the built-in torch.profiler.profile gives a user-friendly strategy to collect efficiency information. There are 2 choices which are supplied to the builders:

• Use the Profiler Context Supervisor
• Concentrating on Profiling for particular neural community layers

Profiler Context Supervisor

The a part of the code that we wish to profile may be wrapped inside the with torch.profiler.profile() context supervisor. Within the with assertion, you’ll be able to outline the actions to hint (CPU, CUDA, or each), set a schedule to profile particular coaching steps, and select whether or not to report tensor shapes, reminiscence utilization, or FLOPs. As soon as contained in the context, you will need to name prof.step() on the finish of every iteration to sign the profiler to advance, particularly when a schedule is used.

with profile(
    actions=,
    schedule=torch.profiler.schedule(),
    record_shapes=,
    profile_memory=,
    with_flops=
) as prof:

    ....
    prof.step()

• actions: Specify whether or not to profile the CPU, CUDA or each.
• schedule: Helpful for profiling a number of steps within the coaching loop. If the schedule parameter is used, the profiler must name prof.step() to maneuver to the following step.
• record_shapes: Whether or not to report the shapes of the tensors.
• profile_memory: To seize reminiscence utilization
• with_flops: That is experimental however is used to FLOPs with operators.

Our profiler command modifications to:

with profile(
    actions=[ProfilerActivity.CPU, ProfilerActivity.CUDA],
    schedule=torch.profiler.schedule(wait=1, warmup=1, lively=3, repeat=2),
    record_shapes=True,
    profile_memory=True,
    with_flops=True
) as prof:

Concentrating on Profiling for particular neural community layers

The profiler will also be utilized in a extra focused method to investigate particular layers of a neural community. That is helpful to verify whether or not some particular layer is contributing extra to the efficiency than the opposite layers giving the developer the choice of modifying particular layers. Whereas utilizing that is very simple to make use of, typically, the primary choice works higher. The PyTorch profiler outcomes will also be exported and visualized on a TensorBoard.

profiler.begin()
self.conv2(x)
profiler.cease()

LLMs and Roofline Modeling

Coming to the subject everybody has been ready for – does Roofline Modeling assist with LLM efficiency calculation? The quick reply is sure.

LLMs are complicated neural community architectures with billions of parameters and the huge datasets that they course of. Whereas coaching is a really resource-intensive process, inference and nice tuning the mannequin additionally have to be environment friendly.

• Bottlenecks: LLMs throughout inference can undergo from bottlenecks because of the sheer quantity of parameters that it’s working with. These parameters are the weights of the fashions and so they trigger reminiscence bandwidth points. Utilizing Roofline Modeling, the precise layers may be profiled for the bottlenecks.
• {Hardware} choice: As most organizations fine-tune current fashions quite than coaching them from scratch, selecting the best infrastructure is essential for managing prices. This underscores the significance of selecting optimum infrastructure for coaching. For instance, selecting the {hardware} in accordance with your LLM structure or optimizing your mannequin to run on a selected structure can lower coaching and inference prices.

Conclusion

The Roofline Mannequin gives a strong visible evaluation of software efficiency optimization. By visualizing the appliance efficiency throughout reminiscence and compute, a transparent steerage is supplied in selecting one of the best ways to strategy optimizations. Whereas this text solely thought-about Naive Roofline Fashions, there are extra superior methods comparable to Hierarchical Roofline Fashions or including ceilings for particular compute optimizations.

References

[1] https://docs.nersc.gov/tools/performance/roofline/

[2] https://docs.nvidia.com/nsight-compute/NsightComputeCli/index.html

[3] https://github.com/pytorch/examples/tree/main/imagenet

[4] https://developer.nvidia.com/nsight-systems