Related papers: Faster Multiplication for Long Binary Polynomials
We present a finite-difference method for the topology optimization of permanent magnets that is based on the FFT accelerated computation of the stray-field. The presented method employs the density approach for topology optimization and…
We propose a new algorithm for multiplying dense polynomials with integer coefficients in a parallel fashion, targeting multi-core processor architectures. Complexity estimates and experimental comparisons demonstrate the advantages of this…
A new transform over finite fields, the finite field Hartley transform (FFHT), was recently introduced and a number of promising applications on the design of efficient multiple access systems and multilevel spread spectrum sequences were…
The discrete Fourier transform (DFT) is widely employed for multi-beam digital beamforming. The DFT can be efficiently implemented through the use of fast Fourier transform (FFT) algorithms, thus reducing chip area, power consumption,…
Discrete cosine transform (DCT) and other Fourier-related transforms have broad applications in scientific computing. However, off-the-shelf high-performance multi-dimensional DCT (MD DCT) libraries are not readily available in parallel…
In this short paper, the authors report a new computational approach in the context of Density Functional Theory (DFT). It is shown how it is possible to speed up the self-consistent cycle (iteration) characterizing one of the most…
The Number Theoretic Transform (NTT) is an indispensable tool for computing efficient polynomial multiplications in post-quantum lattice-based cryptography. It has strong resemblance with the Fast Fourier Transform (FFT), which is the most…
We develop an automated framework for proving lower bounds on the bilinear complexity of matrix multiplication over finite fields. Our approach systematically combines orbit classification of the restricted first matrix and dynamic…
The paper discusses the construction of high dimensional spatial discretizations for arbitrary multivariate trigonometric polynomials, where the frequency support of the trigonometric polynomial is known. We suggest a construction based on…
We explore new approaches for finding matrix multiplication algorithms in the commutative setting by adapting the flip graph technique: a method previously shown to be effective for discovering fast algorithms in the non-commutative case.…
Computing discrete logarithms in finite fields is a main concern in cryptography. The best algorithms in large and medium characteristic fields (e.g., {GF}$(p^2)$, {GF}$(p^{12})$) are the Number Field Sieve and its variants (special,…
Low-bit quantized neural networks are of great interest in practical applications because they significantly reduce the consumption of both memory and computational resources. Binary neural networks are memory and computationally efficient…
We present a new library for parallel distributed Fast Fourier Transforms (FFT). The importance of FFT in science and engineering and the advances in high performance computing necessitate further improvements. AccFFT extends existing FFT…
This paper evaluates the efficacy of recent commercial processing-in-memory (PIM) solutions to accelerate fast Fourier transform (FFT), an important primitive across several domains. Specifically, we observe that efficient implementations…
We give several new algorithms for dense polynomial multiplication based on the Kronecker substitution method. For moderately sized input polynomials, the new algorithms improve on the performance of the standard Kronecker substitution by a…
We present a new algorithm for computing $m$-th roots over the finite field $\F_q$, where $q = p^n$, with $p$ a prime, and $m$ any positive integer. In the particular case $m=2$, the cost of the new algorithm is an expected $O(\M(n)\log (p)…
Symmetric Nonnegative Matrix Factorization (SNMF) models arise naturally as simple reformulations of many standard clustering algorithms including the popular spectral clustering method. Recent work has demonstrated that an elementary…
We present new algorithms for computing the low $n$ bits or the high $n$ bits of the product of two $n$-bit integers. We show that these problems may be solved in asymptotically 75% of the time required to compute the full $2n$-bit product,…
The Fast Reciprocal Square Root Algorithm is a well-established approximation technique consisting of two stages: first, a coarse approximation is obtained by manipulating the bit pattern of the floating point argument using integer…
We design new polynomials for representing threshold functions in three different regimes: probabilistic polynomials of low degree, which need far less randomness than previous constructions, polynomial threshold functions (PTFs) with…