Related papers: Online Alignment and Addition in Multi-Term Floati…

Floating point multiplication is one of the crucial operations in many application domains such as image processing, signal processing etc. But every application requires different working features. Some need high precision, some need low…

Multiple-precision floating-point branch-free algorithms can significantly accelerate multi-component arithmetic implemented by combining hardware-based binary64 and binary32, particularly for triple- and quadruple-precision computations.…

Motivated by the importance of floating-point computations, we study the problem of securely and accurately summing many floating-point numbers. Prior work has focused on security absent accuracy or accuracy absent security, whereas our…

The study addresses the problem of precision in floating-point (FP) computations. A method for estimating the errors which affect intermediate and final results is proposed and a summary of many software simulations is discussed. The basic…

Ootomo, Ozaki, and Yokota [Int. J. High Perform. Comput. Appl., 38 (2024), p. 297-313] have proposed a strategy to recast a floating-point matrix multiplication in terms of integer matrix products. The factors A and B are split into integer…

Minimization of computational errors in the fixed-point data path is often difficult task. Many signal processing algorithms use chains of consecutive additions. The analyzing technique that can be applied to fixed-point data path synthesis…

I present two new methods for exactly summing a set of floating-point numbers, and then correctly rounding to the nearest floating-point number. Higher accuracy than simple summation (rounding after each addition) is important in many…

Debugging accumulation of floating-point errors is hard; ideally, computer should track it automatically. Here we consider twofold approximation of an exact real with value + error pair of floating-point numbers. Normally, value + error sum…

Reducing hardware overhead of neural networks for faster or lower power inference and training is an active area of research. Uniform quantization using integer multiply-add has been thoroughly investigated, which requires learning many…

We present a second-order recursive Fermi-operator expansion scheme using mixed precision floating point operations to perform electronic structure calculations using tensor core units. A performance of over 100 teraFLOPs is achieved for…

One of the crucial issues in federated learning is how to develop efficient optimization algorithms. Most of the current ones require full device participation and/or impose strong assumptions for convergence. Different from the widely-used…

We study the multiple-precision addition of two positive floating-point numbers in base 2, with exact rounding, as specified in the MPFR library, i.e. where each number has its own precision. We show how the best possible complexity (up to…

The escalating scale of Large Language Models (LLMs) necessitates efficient adaptation techniques. Model merging has gained prominence for its efficiency and controllability. However, existing merging techniques typically serve as post-hoc…

In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…

This work proposes a mathematically founded mixed precision accumulation strategy for the inference of neural networks. Our strategy is based on a new componentwise forward error analysis that explains the propagation of errors in the…

Floating-point round-off errors are ubiquitous in numerically intensive programs arising in fields such as scientific computing and optimization. As floating-point errors potentially lead to unexpected and catastrophic program failures, one…

Follow-up experimental designs are popularly used in industry. In many follow-up designs, some additional factors with two or three levels may be added in the follow-up stage since they are quite important but may be neglected in the first…

Model merging has emerged as a cost-efficient approximation to multitask learning. Among merging strategies, task arithmetic is notable for its simplicity and effectiveness. In this work, we provide a theoretical motivation for task vectors…

In this paper, an improved GEF fast addition algorithm is proposed. The proposed algorithm reduces time and memory space. In this algorithm, carry is calculated on the basis of arrival timing of the operand's bits without overhead of…

Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…