Related papers: Radix Conversion for IEEE754-2008 Mixed Radix Floa…
This article is concerned with the efficient computation of modular matrix multiplication C=AB mod p, a key kernel in computer algebra. We focus on floating-point arithmetic, which allows for using efficient matrix multiplication libraries.…
Round-off errors arising from the difference between real numbers and their floating-point representation cause the control flow of conditional floating-point statements to deviate from the ideal flow of the real-number computation. This…
Quantum algorithms to solve practical problems in quantum chemistry, materials science, and matrix inversion often involve a significant amount of arithmetic operations which act on a superposition of inputs. These have to be compiled to a…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Finite precision computations using digital computers involve the following inherent errors: (1) Round-off error of finite precision computations (2) Binary computer arithmetic precludes exact number representation of traditional decimal…
Renewed interest in mixed-precision algorithms has emerged due to growing data capacity and bandwidth concerns, as well as the advancement of GPUs, which enable significant speedup for low precision arithmetic. In light of this, we propose…
Errors in floating-point programs can lead to severe consequences, particularly in critical domains such as military, aerospace, and financial systems, making their repair a crucial research problem. In practice, some errors can be fixed…
This work describes methodologies to successfully implement the Implicit Monte Carlo (IMC) scheme for thermal radiative transfer in reduced-precision floating-point arithmetic. The methods used can be broadly categorized into scaling…
We obtain an exact formula for the Fourier transform of multiradial functions, i.e., functions of the form $\Phi(x)=\phi(|x_1|, \dots, |x_m|)$, $x_i\in \mathbf R^{n_i}$, in terms of the Fourier transform of the function $\phi$ on $\mathbf…
This study reexamines diffusive representations for fractional integrals with the goal of pioneering new variants of such representations. These variants aim to offer highly efficient numerical algorithms for the approximate computation of…
Half precision (FP16) promises to double FFT throughput on GPUs, but the prevailing view is that its 10-bit mantissa makes it unsuitable for radar-grade signal processing. We show this framing is wrong on Apple Silicon: the binding…
Low-cost embedded processors such as the ESP32 (Xtensa LX6, 32-bit dual-core, 240 MHz) are increasingly used in edge computing applications that require real-time physical simulation, sensor fusion, and control systems. Although the ESP32…
Traditional optimization methods rely on the use of single-precision floating point arithmetic, which can be costly in terms of memory size and computing power. However, mixed precision optimization techniques leverage the use of both…
The geodesic ray transform, the mixed ray transform and the transverse ray transform of a tensor field on a manifold can all be seen as what we call mixing ray transforms, compositions of the geodesic ray transform and an invertible linear…
Given a point set $\mathcal{P}$ and a plane perfect matching $\mathcal{M}$ on $\mathcal{P}$, a flip is an operation that replaces two edges of $\mathcal{M}$ such that another plane perfect matching on $\mathcal{P}$ is obtained. Given two…
Multipliers are widely-used arithmetic operators in digital signal processing and machine learning circuits. Due to their relatively high complexity, they can have high latency and be a significant source of power consumption. One strategy…
Scientific computing applications, such as computational fluid dynamics and climate modeling, typically rely on 64-bit double-precision floating-point operations, which are extremely costly in terms of computation, memory, and energy. While…
We find a formula for the resolution of fixed points in extensions of permutation orbifold conformal field theories by its (half-)integer spin simple currents. We show that the formula gives a unitary and modular invariant S matrix.
In this work, we provide energy-efficient architectural support for floating point accuracy. Our goal is to provide accuracy that is far greater than that provided by the processor's hardware floating point unit (FPU). Specifically, for…
An improvement on precision of recursive function simulation in IEEE floating point standard is presented. It is shown that the average of rounding towards negative infinite and rounding towards positive infinite yields a better result than…