By Iain T. Adamson
Presents a proper description of set conception in line with the Von Neumann-Bernays-Godel axiomatic method utilizing the idea that of sessions. Covers the basis of the speculation, family members, ordinals, cardinals, and the axiom of selection. Paper. DLC: Set idea.
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Here, we chose the number of Euclidean distance computations performed as our metric for computational complexity. Since the tree creation phase does not compute any distances but performs mainly dot product computations and comparisons, we introduce distance computation equivalents (DCEs) to obtain a unified metric for both parts which combines several operations which are computationally equivalent. 1 shows the profiling results of the computational complexity of the filtering algorithm broken down into clustering and pre-processing phases for different working sets.
However, our implementation of the filtering algorithm requires more memory compared to Lloyd’s algorithm. This is mainly due to the increased memory space required to store the data points in the kd-tree structure. We can conclude that the availability of on-chip BRAM resources is the limiting factor in scaling this algorithm through increased parallelism, but the advantage of its RTL implementation in terms of computational resources is compelling. 2 HLS Designs We compare the performance of both HLS to both RTL designs based on different metrics: clock cycles count per iteration (through RTL simulations), execution time per iteration (includes the clock period), resource usage and AT product (in logic slices × ms).
6 Summary This chapter presents a comparative case study for a C-to-FPGA flow using Xilinx Vivado HLS as an exemplary state-of-the-art tool. Our test cases are two alternative algorithms for K -means clustering, referred to as Lloyd’s algorithm and the filtering algorithm. The former is a data flow-centric brute-force approach and has regular control flow and regular memory accesses, whereas the implementation of the filtering algorithm uses dynamic memory management and is based on recursive traversal of a pointer-linked tree structure.
A Set Theory Workbook by Iain T. Adamson