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Frugal computing is becoming an important topic for environmental reasons. In this context, several techniques have been proposed to reduce the storage of scientific data by dedicated compression methods specially tailored for arrays of…

Scientific machine learning (SciML) has emerged as a versatile approach to address complex computational science and engineering problems. Within this field, physics-informed neural networks (PINNs) and deep operator networks (DeepONets)…

We propose a novel floating-point encoding scheme that builds on prior work involving fixed-point encodings. We encode floating-point numbers using Two's Complement fixed-point mantissas and Two's Complement integral exponents. We used our…

Significant inaccuracy often occurs during the process of mathematical calculation due to the digit limitation of floating point, which may lead to catastrophic loss. Normally, people believe that adjustment of floating-point precision is…

Scientific computing programs often undergo aggressive compiler optimization to achieve high performance and efficient resource utilization. While performance is critical, we also need to ensure that these optimizations are correct. In this…

In recent years fused-multiply-add (FMA) units with lower-precision multiplications and higher-precision accumulation have proven useful in machine learning/artificial intelligence applications, most notably in training deep neural networks…

In this paper, we propose a mixed-precision convolution unit architecture which supports different integer and floating point (FP) precisions. The proposed architecture is based on low-bit inner product units and realizes higher precision…

Geometric predicates are at the core of many algorithms, such as the construction of Delaunay triangulations, mesh processing and spatial relation tests. These algorithms have applications in scientific computing, geographic information…

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…

Today, almost all computer systems use IEEE-754 floating point to represent real numbers. Recently, posit was proposed as an alternative to IEEE-754 floating point as it has better accuracy and a larger dynamic range. The configurable…

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…

Modern computing clusters offer specialized hardware for reduced-precision arithmetic that can speed up the time to solution significantly. This is possible due to a decrease in data movement, as well as the ability to perform arithmetic…

Conventional hardware-friendly quantization methods, such as fixed-point or integer, tend to perform poorly at very low word sizes as their shrinking dynamic ranges cannot adequately capture the wide data distributions commonly seen in…

Floating-point programs form the foundation of modern science and engineering, providing the essential computational framework for a wide range of applications, such as safety-critical systems, aerospace engineering, and financial analysis.…

Floating-point square-root computation is a power- and delay-critical operation in edge-AI, signal-processing, and embedded systems. Conventional implementations typically rely on multipliers or iterative pipelines, resulting in increased…

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 investigate the use of half-precision floating-point numbers (FP16) in mixed-precision linear solvers for lattice QCD simulations. Since the emergence of GPUs for general-purpose, mixed-precision algorithms that combine single-precision…

In the early days of computing, severe memory constraints made it necessary to use lower floating-point precision. As hardware capabilities have advanced, modern systems, particularly in computational statistics and scientific computing,…

In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…

The state-of-the-art hardware platforms for training Deep Neural Networks (DNNs) are moving from traditional single precision (32-bit) computations towards 16 bits of precision -- in large part due to the high energy efficiency and smaller…