CUDA Atomic Sum Reduction

mediumFREEReductions, Sync & AtomicsCUDA Basics with Numba

Problem Statement

Sum a 1D array into a single value using cuda.atomic.add: every thread atomically adds its element into out[0].

Background

When many threads update the same location, plain += races. cuda.atomic.add(out, 0, value) performs a read-modify-write that can't be interrupted, so no updates are lost. Initialize the accumulator to 0 before launching.

Your Task

Implement atomic_sum_kernel and run(n=4096) returning whether out[0] matches x.sum().

How it is tested

Your solution must define a top-level function run(...) that allocates the inputs, copies them to the GPU, launches your @cuda.jit kernel, and returns a Python bool from np.allclose(gpu_result, reference). The grader prints run(...); the expected output is True.

Example

Input

n = 4096

Output

True

Reasoning

The input n = 4096 is used to create a 1D array of size 4096 with random values.
The atomic_sum_kernel function is launched with multiple threads, each of which atomically adds its corresponding element from the array to out[0] using cuda.atomic.add.
The atomic addition operation ensures that all updates to out[0] are properly synchronized, avoiding any data races or lost updates, resulting in the correct sum of the array elements: $out[0] = \sum_{i=0}^{n-1} x_i$ .
The final output is True because the sum computed using cuda.atomic.add matches the reference sum computed using x.sum(), i.e., np.allclose(gpu_result, reference) evaluates to True.

Constraints

cuda.atomic.add(out, 0, x[i]) for each in-range thread
Initialize the device accumulator to 0
Compare with a tolerant atol (float32 atomic order varies)

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Concept primer

Background Knowledge

The problem involves using CUDA, a parallel computing platform developed by NVIDIA, to perform a reduction operation on a 1D array. In this context, reduction refers to the process of combining all elements of an array into a single value, in this case, by summing them. The key challenge here is that many threads are updating the same location, which can lead to race conditions if not handled properly. A race condition occurs when the outcome of a program depends on the relative timing of threads, leading to unpredictable results.

To address this issue, CUDA provides atomic operations, which are guaranteed to be executed without interruption. In this problem, we will use cuda.atomic.add to perform an atomic addition, ensuring that each thread's update is properly accounted for. The use of atomic operations is crucial in parallel programming, as it allows for safe and efficient updates of shared variables. Understanding how to use atomic operations is essential for solving problems that involve concurrent access to shared resources.

The problem also involves using Numba, a Python library that provides a high-performance, just-in-time compiler for Python and NumPy code. Numba's @cuda.jit decorator is used to define CUDA kernels, which are functions that run on the GPU. The kernel will be launched with multiple threads, each of which will execute the same code. The threads will cooperate to perform the reduction operation, using atomic operations to ensure that the result is accurate.

Algorithm/Approach

The general approach to solving this problem involves using a parallel reduction algorithm, where multiple threads cooperate to reduce the array to a single value. The key steps involve:

Initializing the accumulator variable to 0
Launching a CUDA kernel with multiple threads, each of which will execute the same code
Using atomic operations to update the accumulator variable
Verifying that the result matches the expected value

The parallel reduction algorithm can be implemented using a variety of techniques, including thread block-based approaches, where each thread block is responsible for reducing a portion of the array.

Step-by-Step Strategy

To implement the solution, follow these steps:

Import the necessary libraries, including numba and numpy.
Define the atomic_sum_kernel function, which will be decorated with @cuda.jit to indicate that it is a CUDA kernel.
Initialize the accumulator variable to 0 before launching the kernel.
Launch the kernel with multiple threads, each of which will execute the atomic_sum_kernel function.
Use cuda.atomic.add to update the accumulator variable within the kernel.
Verify that the result matches the expected value by comparing it to the result of x.sum().

Common Pitfalls

When implementing the solution, watch out for the following common pitfalls:

Failing to initialize the accumulator variable to 0 before launching the kernel
Using plain += instead of cuda.atomic.add to update the accumulator variable
Launching the kernel with too few threads, which can lead to poor performance
Failing to verify that the result matches the expected value

Time & Space Complexity

The expected time complexity of the solution is $O(n)$ , where $n$ is the length of the input array. This is because each thread will execute a constant amount of work, and the number of threads is proportional to the length of the input array. The space complexity is $O(1)$ , since we only need to store a single accumulator variable. Note that the actual performance of the solution will depend on the specific hardware and implementation details.

solution.py

Python 3.13

GPU · T4

Test results