Related papers: A floating point division unit based on Taylor-Ser…
Simple floating point operations like addition or multiplication on normalized floating point values can be computed by current AMD and Intel processors in three to five cycles. This is different for denormalized numbers, which appear when…
The letter proposes an adaptive model reduction approach based on tensor decomposition to speed up time-domain power system simulation. Taylor series expansion of a power system dynamic model is calculated around multiple equilibria…
We present a novel right-to-left long division algorithm based on the Montgomery modular multiply, consisting of separate highly efficient loops with simply carry structure for computing first the remainder (x mod q) and then the quotient…
This paper provides modified Distributed Arithmetic based technique to compute sum of products saving appreciable number of Multiply And accumulation blocks and this consecutively reduces circuit size. In this technique multiplexer based…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
We derive and discuss a technique for manipulating power series which is complementary to standard procedures. We begin with the translation operator, but we express the operator as an infinite product instead of expanding it as a series…
We consider space-saving versions of several important operations on univariate polynomials, namely power series inversion and division, division with remainder, multi-point evaluation, and interpolation. Now-classical results show that…
Multiplication is a core operation in modern neural network (NN) computations, contributing significantly to energy consumption. The linear-complexity multiplication (L-Mul) algorithm is specifically proposed as an approximate…
We construct new algorithms from scratch, which use the fourth order cumulant of stochastic variables for the cost function. The multiplicative updating rule here constructed is natural from the homogeneous nature of the Lie group and has…
This paper presents a novel approach for performing computations using Look-Up Tables (LUTs) tailored specifically for Compute-in-Memory applications. The aim is to address the scalability challenges associated with LUT-based computation by…
A novel parallel algorithm for matrix multiplication is presented. The hyper-systolic algorithm makes use of a one-dimensional processor abstraction. The procedure can be implemented on all types of parallel systems. It can handle…
The method of Taylor series expansion is used to develop a numerical solution to the reactor point kinetics equations. It is shown that taking a first order expansion of the neutron density and precursor concentrations at each time step…
The aim of this paper is to analyse the gain of the update algorithm associated to the recently proposed D-iteration: the D-iteration is a fluid diffusion based new iterative method. It exploits a simple intuitive decomposition of the…
Multiplication is indispensable and is one of the core operations in many modern applications including signal processing and neural networks. Conventional right-to-left (RL) multiplier extensively contributes to the power consumption, area…
Fast convergent, accurate, computationally efficient, parallelizable, and robust matrix inversion and parameter estimation algorithms are required in many time-critical and accuracy-critical applications such as system identification,…
The new generation of machine learning processors have evolved from multi-core and parallel architectures that were designed to efficiently implement matrix-vector-multiplications (MVMs). This is because at the fundamental level, neural…
We propose a method to examine how a parton shower sums large logarithms. In this method, one works with an appropriate integral transform of the distribution for the observable of interest. Then, one reformulates the parton shower so as to…
We propose and analyse a numerical integrator that computes a low-rank approximation to large time-dependent matrices that are either given explicitly via their increments or are the unknown solution to a matrix differential equation.…
In this paper, we contribute operator-splitting methods improved by the Zassenhaus product for the numerical solution of linear partial differential equations. We address iterative splitting methods, that can be improved by means of the…
In this paper, we propose an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication. The proposed work will of great importance in applications which requires variable…