CUDA Atomic Histogram
Problem Statement
Build a histogram of values in [0, 1) into nbins bins using atomic adds. Each thread computes its bin index and does cuda.atomic.add(hist, b, 1).
Background
Many threads land in the same bin, so the increment must be atomic. Compute the bin as int(x[i] * nbins), clamped into [0, nbins-1], then atomically bump that counter.
Your Task
Implement hist_kernel and run(n=4096, nbins=10) returning whether the GPU histogram matches np.bincount.
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:
n = 4096, nbins = 10
True
- The input values
n = 4096andnbins = 10are used to allocate an array ofnrandom values between 0 and 1, and a histogram array of sizenbins. - Each thread in the
hist_kernelcomputes its bin index as b=min(max(int(x[i]⋅nbins),0),nbins−1), where x[i] is the ith value in the input array. - The threads then perform an atomic add operation on the corresponding bin in the histogram array using
cuda.atomic.add(hist, b, 1), effectively counting the number of values that fall into each bin. - The resulting histogram is compared to a reference histogram computed using
np.bincount, and the function returnsTrueif the two histograms are close (i.e.,np.allclose(gpu_result, reference)), indicating that the GPU histogram matches the expected result.
Constraints:
- b = int(x[i] * nbins), clamped to [0, nbins-1]
- cuda.atomic.add(hist, b, 1) on an int32 histogram
- Inputs are in [0, 1)
Background Knowledge
The problem involves building a histogram of values using CUDA, a parallel computing platform developed by NVIDIA. To understand this problem, it's essential to have a basic knowledge of parallel programming and GPU architecture. In parallel programming, multiple threads or processes execute simultaneously, improving the overall performance of the system. In the context of CUDA, the GPU (Graphics Processing Unit) is used to perform computations, and the CPU (Central Processing Unit) is used to manage the execution of the program.
The problem also involves atomic operations, which are essential in parallel programming to ensure that multiple threads access shared resources safely. An atomic operation is a sequence of operations that is executed as a single, indivisible unit. In this problem, atomic adds are used to update the histogram bins. The cuda.atomic.add function is used to perform an atomic addition operation, which ensures that the update operation is thread-safe.
The problem requires a good understanding of histogram construction and binning. A histogram is a graphical representation of the distribution of a set of values. In this problem, the values are in the range [0, 1), and the goal is to build a histogram with nbins bins. The bin index is computed as int(x[i] * nbins), clamped into [0, nbins-1]. This means that each value is mapped to a bin based on its value, and the bin index is used to update the corresponding counter in the histogram.
Algorithm/Approach
The general approach to solving this problem involves the following steps:
- Allocate memory for the input array and the histogram on the GPU
- Launch a CUDA kernel that computes the bin index for each value in the input array
- Use atomic adds to update the corresponding bin in the histogram
- Copy the histogram from the GPU to the CPU and compare it with the reference histogram computed using np.bincount
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