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

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…

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…

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…

Large neural networks spend most computation on floating point tensor multiplications. In this work, we find that a floating point multiplier can be approximated by one integer adder with high precision. We propose the linear-complexity…

Reasoning about floating-point arithmetic is notoriously hard. While static and dynamic analysis techniques or program repair have made significant progress, more work is still needed to make them relevant to real-world code. On the…

Numerical codes that require arbitrary precision floating point (APFP) numbers for their core computation are dominated by elementary arithmetic operations due to the super-linear complexity of multiplication in the number of mantissa bits.…

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…

With the proliferation of embedded systems requiring intelligent behavior, custom number systems to optimize performance per Watt of the entire system become essential components for successful commercial products. We present the Universal…

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…

Compression of floating-point data will play an important role in high-performance computing as data bandwidth and storage become dominant costs. Lossy compression of floating-point data is powerful, but theoretical results are needed to…

In this work, approximate eight-bit floating-point operations performed using simple integer operations is discussed. For two-bit mantissa formats, faithful rounding can always be obtained for the considered operations. For all operations,…

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…

In the field of High Performance Computing, communications among processes represent a typical bottleneck for massively parallel scientific applications. Object of this research is the development of a network interface card with specific…

The wide adoption of DNNs has given birth to unrelenting computing requirements, forcing datacenter operators to adopt domain-specific accelerators to train them. These accelerators typically employ densely packed full precision…

Reduced precision computation for deep neural networks is one of the key areas addressing the widening compute gap driven by an exponential growth in model size. In recent years, deep learning training has largely migrated to 16-bit…

The problem of exactly summing n floating-point numbers is a fundamental problem that has many applications in large-scale simulations and computational geometry. Unfortunately, due to the round-off error in standard floating-point…

In this paper, we propose an architecture/methodology for making FPGAs suitable for integer as well as variable precision floating point multiplication. The proposed work will of great importance in applications which requires variable…

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…

We devise a variable precision floating-point arithmetic by exploiting the framework provided by the Infinity Computer. This is a computational platform implementing the Infinity Arithmetic system, a positional numeral system which can…

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…