Related papers: Floating-floating point: a highly accurate number …

Floating point division, even though being an infrequent operation in the traditional sense, is indis- pensable when it comes to a range of non-traditional applications such as K-Means Clustering and QR Decomposition just to name a few. In…

Mixed precision training (MPT) is becoming a practical technique to improve the speed and energy efficiency of training deep neural networks by leveraging the fast hardware support for IEEE half-precision floating point that is available in…

Deep neural networks (DNNs) are powerful for cognitive tasks such as image classification, object detection, and scene segmentation. One drawback however is the significant high computational complexity and memory consumption, which makes…

Fluid antenna system promises to obtain enormous diversity in the small space of a mobile device by switching the position of the radiating element to the most desirable position from a large number of prescribed locations of the given…

The use of reduced and mixed precision computing has gained increasing attention in high-performance computing (HPC) as a means to improve computational efficiency, particularly on modern hardware architectures like GPUs. In this work, we…

We propose a new instruction (FPADDRE) that computes the round-off error in floating-point addition. We explain how this instruction benefits high-precision arithmetic operations in applications where double precision is not sufficient.…

Floating-point arithmetic is error-prone and unintuitive. Floating-point debuggers instrument programs to monitor floating-point arithmetic at run time and flag numerical issues. They estimate residues, i.e., the difference between actual…

Much recent research is devoted to exploring tradeoffs between computational accuracy and energy efficiency at different levels of the system stack. Approximation at the floating point unit (FPU) allows saving energy by simply reducing the…

Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying…

We analyse the forward error in the floating point summation of real numbers, from algorithms that do not require recourse to higher precision or better hardware. We derive informative explicit expressions, and new deterministic and…

Generating 2-by-2 unitary matrices in floating-precision arithmetic is a delicate task. One way to reduce the accumulation error is to use less floating-point operations to compute each of the entries in the 2-by-2 unitary matrix. This…

One of the major bottlenecks in high-resolution Earth Observation (EO) space systems is the downlink between the satellite and the ground. Due to hardware limitations, on-board power limitations or ground-station operation costs, there is a…

There is a recent interest in neural network (NN)-based communication algorithms which have shown to achieve (beyond) state-of-the-art performance for a variety of problems or lead to reduced implementation complexity. However, most work on…

This preliminary white paper proposes a novel 8-bit floating-point data format HiFloat8 (abbreviated as HiF8) for deep learning. HiF8 features tapered precision. For normal value encoding, it provides 7 exponent values with 3-bit mantissa,…

Deep neural networks (DNN) are powerful models for many pattern recognition tasks, yet their high computational complexity and memory requirement limit them to applications on high-performance computing platforms. In this paper, we propose…

Multi-term floating-point addition appears in vector dot-product computations, matrix multiplications, and other forms of floating-point data aggregation. A critical step in multi-term floating point addition is the alignment of fractions…

The typical processors used for scientific computing have fixed-width data-paths. This implies that mathematical libraries were specifically developed to target each of these fixed precisions (binary16, binary32, binary64). However, to…

Solving linear systems is a ubiquitous task in science and engineering. Because directly inverting a large-scale linear system can be computationally expensive, iterative algorithms are often used to numerically find the inverse. To…

Training Deep Neural Networks (DNNs) can be computationally demanding, particularly when dealing with large models. Recent work has aimed to mitigate this computational challenge by introducing 8-bit floating-point (FP8) formats for…

We introduce data structures and algorithms to count numerical inaccuracies arising from usage of floating numbers described in IEEE 754. Here we describe how to estimate precision for some collection of functions most commonly used for…