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Although reliable long precision floating-point arithmetic libraries such as QD and MPFR/GMP are necessary to solve ill-conditioned problems in numerical simulation, long precision BLAS-level computation such as matrix multiplication has…
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.…
We offer a novel approach, MGS (Markov Greedy Sums), to improve the accuracy of low-bitwidth floating-point dot products in neural network computations. In conventional 32-bit floating-point summation, adding values with different exponents…
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…
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…
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…
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…
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…
Attention mechanisms, particularly within Transformer architectures and large language models (LLMs), have revolutionized sequence modeling in machine learning and artificial intelligence applications. To compute attention for increasingly…
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…
In modern computing units, division operations are generally slower than other arithmetic operations and require more resources, such as area and power, than multiplication. To reduce the delay, fast division algorithms use an initial…
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…
The growing demands of the worldwide IT infrastructure stress the need for reduced power consumption, which is addressed in so-called transprecision computing by improving energy efficiency at the expense of precision. For example, reducing…
Mixed-precision computations are a hallmark of the current stage of AI, driving the progress in large language models towards efficient, locally deployable solutions. This article addresses the floating-point computation of…
Low precision data representation is important to reduce storage size and memory access for convolutional neural networks (CNNs). Yet, existing methods have two major limitations: (1) requiring re-training to maintain accuracy for deep…
Nowadays, parallel computing is ubiquitous in several application fields, both in engineering and science. The computations rely on the floating-point arithmetic specified by the IEEE754 Standard. In this context, an elementary brick of…
The fast proliferation of extreme-edge applications using Deep Learning (DL) based algorithms required dedicated hardware to satisfy extreme-edge applications' latency, throughput, and precision requirements. While inference is achievable…
Recent research has shown that large language models (LLMs) can utilize low-precision floating point (FP) quantization to deliver high efficiency while maintaining original model accuracy. In particular, recent works have shown the…
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…
While Deep Neural Networks (DNNs) push the state-of-the-art in many machine learning applications, they often require millions of expensive floating-point operations for each input classification. This computation overhead limits the…