Related papers: Beating Posits at Their Own Game: Takum Arithmetic
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…
Posit has been a promising alternative to the IEEE-754 floating point format for deep learning applications due to its better trade-off between dynamic range and accuracy. However, hardware implementation of posit arithmetic requires…
We propose a new complex block floating-point format to reduce implementation complexity. The new format achieves wordlength reduction by sharing an exponent across the block of samples, and uses box encoding for the shared exponent to…
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…
Dynamic and polymorphic languages attach information, such as types, to run time objects, and therefore adapt the memory layout of values to include space for this information. This makes it difficult to efficiently implement IEEE754…
Spectral analysis plays an important role in detection of damage in structures and deep learning. The choice of a floating-point format plays a crucial role in determining the accuracy and performance of spectral analysis. The IEEE Std…
Modern programmable digital signal processing relies on floating-point numbers for their ease of use. Fixed-point number formats have the potential to save resources and improve execution time, but realising this potential burdens the…
One requirement of maintaining digital information is storage. With the latest advances in the digital world, new emerging media types have required even more storage space to be kept than before. In fact, in many cases it is required to…
Many domains, from deep learning to finance, require compounding real numbers over long sequences, often leading to catastrophic numerical underflow or overflow. We introduce generalized orders of magnitude (GOOMs), a principled extension…
A new deterministic floating-point arithmetic called precision arithmetic is developed to track precision for arithmetic calculations. It uses a novel rounding scheme to avoid excessive rounding error propagation of conventional…
One of the major promises of quantum computing is the realization of SIMD (single instruction - multiple data) operations using the phenomenon of superposition. Since the dimension of the state space grows exponentially with the number of…
The introduction of posit reopened the debate about the utility of IEEE754 in specific domains. In this context, we propose a high-level language (Scala) library that aims to reduce the effort of designing and testing new number…
General matrix multiplication (GEMM) is a ubiquitous computing kernel/algorithm for data processing in diverse applications, including artificial intelligence (AI) and deep learning (DL). Recent shift towards edge computing has inspired…
The accuracy requirements in many scientific computing workloads result in the use of double-precision floating-point arithmetic in the execution kernels. Nevertheless, emerging real-number representations, such as posit arithmetic, show…
Precision tuning or customized precision number representations is emerging, in these recent years, as one of the most promising techniques that has a positive impact on the footprint of programs concerning energy consumption, bandwidth…
To overcome the limitations of conventional floating-point number formats, an interval arithmetic and variable-width storage format called universal number (unum) has been recently introduced. This paper presents the first (to the best of…
An implementation-efficient finite alphabet decoder for polar codes relying on coarsely quantized messages and low-complexity operations is proposed. Typically, finite alphabet decoding performs concatenated compression operations on the…
We report on prime number decomposition by use of the Talbot effect, a well-known phenomenon in classical near field optics whose description is closely related to Gauss sums. The latter are a mathematical tool from number theory used to…
Fault-tolerant capacities quantify the ability of a quantum channel to reliably transmit information when every component of the encoding and decoding procedure is noisy. Earlier work analyzed achievable communication rates under such noise…
The recent advances in machine learning, in general, and Artificial Neural Networks (ANN), in particular, has made smart embedded systems an attractive option for a larger number of application areas. However, the high computational…