Related papers: FFTc: An MLIR Dialect for Developing HPC Fast Four…
To take full advantage of a specific hardware target, performance engineers need to gain control on compilers in order to leverage their domain knowledge about the program and hardware. Yet, modern compilers are poorly controlled, usually…
Fourier transform (FT) plays a crucial role in a broad range of applications, from enhancement, restoration and analysis through to security, compression and manipulation. The Fourier transform (FT) is a process that converts a function…
The Python package fluidfft provides a common Python API for performing Fast Fourier Transforms (FFT) in sequential, in parallel and on GPU with different FFT libraries (FFTW, P3DFFT, PFFT, cuFFT). fluidfft is a comprehensive FFT framework…
In this work, we introduce a definition of the Discrete Fourier Transform (DFT) on Euclidean lattices in $\R^n$, that generalizes the $n$-th fold DFT of the integer lattice $\Z^n$ to arbitrary lattices. This definition is not applicable for…
Given a time series vector, how can we efficiently compute a specified part of Fourier coefficients? Fast Fourier transform (FFT) is a widely used algorithm that computes the discrete Fourier transform in many machine learning applications.…
Image Representation learning via input reconstruction is a common technique in machine learning for generating representations that can be effectively utilized by arbitrary downstream tasks. A well-established approach is using…
We describe a methodology for designing efficient parallel and distributed scientific software. This methodology utilizes sequences of mechanizable algebra--based optimizing transformations. In this study, we apply our methodology to the…
The fast Fourier transform, FFT, is a useful and prevalent algorithm in signal processing. It characterizes the spectral components of a signal, or is used in combination with other operations to perform more complex computations such as…
Fortran is the lingua franca of HPC code development and as such it is crucial that we as a community have open source Fortran compilers capable of generating high performance executables. Flang is LLVM's Fortran compiler and leverages MLIR…
Since the evolution of digital computers, the storage of data has always been in terms of discrete bits that can store values of either 1 or 0. Hence, all computer programs (such as MATLAB), convert any input continuous signal into a…
The Fast Fourier Transform (FFT) is a numerical operation that transforms a function into a form comprised of its constituent frequencies and is an integral part of scientific computation and data analysis. The objective of our work is to…
The nonuniform fast Fourier transform (NUFFT) generalizes the FFT to off-grid data. Its many applications include image reconstruction, data analysis, and the numerical solution of differential equations. We present FINUFFT, an efficient…
Extensive set of tests on different platforms indicated that there is a performance drop of current standard de facto software library for the Discrete Fourier Transform (DFT) in case of large 2D array sizes (larger than 16384x16384).…
Code intelligence plays a key role in transforming modern software engineering. Recently, deep learning-based models, especially Transformer-based large language models (LLMs), have demonstrated remarkable potential in tackling these tasks…
MLIR has become popular since it was open sourced in 2019. A sub-project of LLVM, the flexibility provided by MLIR to represent Intermediate Representations (IR) as dialects at different abstraction levels, to mix these, and to leverage…
Cyclotomic fast Fourier transforms (CFFTs) are efficient implementations of discrete Fourier transforms over finite fields, which have widespread applications in cryptography and error control codes. They are of great interest because of…
Fourier and related transforms is a family of algorithms widely employed in diverse areas of computational science, notoriously difficult to scale on high-performance parallel computers with large number of processing elements (cores). This…
Fast Fourier Transforms (FFTs) are exploited in a wide variety of fields ranging from computer science to natural sciences and engineering. With the rising data production bandwidths of modern FFT applications, judging best which…
This paper details the purpose, difficulties, theory, implementation, and results of developing a Fast Fourier Transform (FFT) using the prime factor algorithm on an embedded system. Many applications analyze the frequency content of…
Density functional theory (DFT) stands as a cornerstone method in computational quantum chemistry and materials science due to its remarkable versatility and scalability. Yet, it suffers from limitations in accuracy, particularly when…