Related papers: Combined Integer and Variable Precision (CIVP) Flo…

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 advancements in quantization have significantly reduced the computational costs of inference in deep learning, training still predominantly relies on complex floating-point arithmetic. Low-precision fixed-point training presents a…

Multiplication of n-digit integers by long multiplication requires O(n^2) operations and can be time-consuming. In 1970 A. Schoenhage and V. Strassen published an algorithm capable of performing the task with only O(n log(n)) arithmetic…

We present the analysis of various FPGA design implementations of a Montgomery Modular Multiplier, compatible with the BLS12-381 elliptic curve, using the Coarsely Integrated Operand Scanning approach of working with complete partial…

GPU has a significantly higher performance in single-precision computing than that of double precision. Hence, it is important to take a maximal advantage of the single precision in the CG inverter, using the mixed precision method. We have…

Given the importance of floating-point~(FP) performance in numerous domains, several new variants of FP and its alternatives have been proposed (e.g., Bfloat16, TensorFloat32, and Posits). These representations do not have correctly rounded…

This paper presents the first comprehensive empirical study demonstrating the efficacy of the Brain Floating Point (BFLOAT16) half-precision format for Deep Learning training across image classification, speech recognition, language…

Deep convolutional neural network (CNN) inference requires significant amount of memory and computation, which limits its deployment on embedded devices. To alleviate these problems to some extent, prior research utilize low precision…

This paper presents an approximate signed multiplier architecture that incorporates a sign-focused compressor, specifically designed for edge detection applications in machine learning and signal processing. The multiplier incorporates two…

Low-precision is the first order knob for achieving higher Artificial Intelligence Operations (AI-TOPS). However the algorithmic space for sub-8-bit precision compute is diverse, with disruptive changes happening frequently, making FPGAs a…

In numeric-intensive computations, it is well known that the execution of floating-point programs is imprecise as floating-point arithmetic incurs round-off errors. Although round-off errors are small for a single floating-point operation,…

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…

Numerical accuracy of floating point computation is a well studied topic which has not made its way to the end-user in scientific computing. Yet, it has become a critical issue with the recent requirements for code modernization to harness…

It is now a noticeable trend in High Performance Computing that the systems are becoming more and more heterogeneous. Compute nodes with a host CPU are being equipped with accelerators, the latter being a GPU or FPGA cards or both. In many…

The advent of computationally demanding algorithms and high data rate instruments in new space applications pushes the space industry to explore disruptive solutions for on-board data processing. We examine heterogeneous computing…

Recent advances in deep learning (DL) have led to a shift from traditional 64-bit floating point (FP64) computations toward reduced-precision formats, such as FP16, BF16, and 8- or 16-bit integers, combined with mixed-precision arithmetic.…

Arbitrary-precision integer multiplication is the core kernel of many applications in simulation, cryptography, etc. Existing acceleration of arbitrary-precision integer multiplication includes CPUs, GPUs, FPGAs, and ASICs. Among these…

The technique for hardware multiplication based upon Fourier transformation has been introduced. The technique has the highest efficiency on multiplication units with up to 8 bit range. Each multiplication unit is realized on base of the…

The advent of switches with programmable dataplanes has enabled the rapid development of new network functionality, as well as providing a platform for acceleration of a broad range of application-level functionality. However, existing…

Given the current trend of increasing size and complexity of machine learning architectures, it has become of critical importance to identify new approaches to improve the computational efficiency of model training. In this context, we…