Related papers: Efficient implementation of elementary functions i…
Large language models (LLMs) have been widely applied but face challenges in efficient inference. While quantization methods reduce computational demands, ultra-low bit quantization with arbitrary precision is hindered by limited GPU Tensor…
Counters are a fundamental building block for networking applications such as load balancing, traffic engineering, and intrusion detection, which require estimating flow sizes and identifying heavy hitter flows. Existing works suggest…
We introduce a numerical method for the approximation of functions which are analytic on compact intervals, except at the endpoints. This method is based on variable transforms using particular parametrized exponential and…
The natural exponential function is widely used in modeling many engineering and scientific systems. It is also an integral part of many neural network activation function such as sigmoid, tanh, ELU, RBF etc. Dedicated hardware accelerator…
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with…
This paper presents a novel method for generating a single polynomial approximation that produces correctly rounded results for all inputs of an elementary function for multiple representations. The generated polynomial approximation has…
In our recent publication [1] we presented an exponential series approximation suitable for highly accurate computation of the complex error function in a rapid algorithm. In this Short Communication we describe how a simplified…
In this paper we present an abstraction-refinement approach to Satisfiability Modulo the theory of transcendental functions, such as exponentiation and trigonometric functions. The transcendental functions are represented as uninterpreted…
Compiling files individually lends itself well to parallelization, but forces the compiler to operate on incomplete programs. State-of-the-art points-to analyses guarantee sound solutions only for complete programs, requiring summary…
We review existing methods for implementing smooth functions f(A) of a sparse Hermitian matrix A on a quantum computer, and analyse a further combination of these techniques which has some advantages of simplicity and resource consumption…
We present Epsilon, a system for general convex programming using fast linear and proximal operators. As with existing convex programming frameworks, users specify convex optimization problems using a natural grammar for mathematical…
Bessel functions are critical in scientific computing for applications such as machine learning, protein structure modeling, and robotics. However, currently, available routines lack precision or fail for certain input ranges, such as when…
This paper presents a novel boundary-optimized fast Fourier extension algorithm for efficient approximation of non-periodic functions. The proposed methodology constructs periodic extensions through strategic utilization of boundary…
The increasing adoption of approximate computing in deep neural network accelerators (AxDNNs) promises significant energy efficiency gains. However, permanent faults in AxDNNs can severely degrade their performance compared to their…
We describe a method for calculating the roots of special functions satisfying second order linear ordinary differential equations. It exploits the recent observation that the solutions of a large class of such equations can be represented…
We consider the question of efficient estimation in the tails of Gaussian copulas. Our special focus is estimating expectations over multi-dimensional constrained sets that have a small implied measure under the Gaussian copula. We propose…
Several paradigms for declarative problem solving start from a specification in a high-level language, which is then transformed to a low-level language, such as SAT or SMT. Often, this transformation includes a "grounding" step to remove…
Branch cuts in complex functions in combination with signed zero and signed infinity have important uses in fracture mechanics, jet flow and aerofoil analysis. We present benchmarks for validating Fortran 2008 complex functions - LOG, SQRT,…
The evaluation of a matrix exponential function is a classic problem of computational linear algebra. Many different methods have been employed for its numerical evaluation [Moler C and van Loan C 1978 SIAM Review 20 4], none of which…
We present analytical formulas for the calculation of the two-center two-electron integrals in the basis of Slater geminals and products of Slater orbitals. Our derivation starts with establishing a inhomogeneous fourth-order ordinary…