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Presented here are algorithms for converting between (decimal) scientific-notation and (binary) IEEE-754 double-precision floating-point numbers. By employing a rounding integer quotient operation these algorithms are much simpler than…
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,…
Data files often consist of numbers having only a few significant decimal digits, whose information content would allow storage in only 32 bits. However, we may require that arithmetic operations involving these numbers be done with 64-bit…
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…
Iterative solvers are frequently used in scientific applications and engineering computations. However, the memory-bound Sparse Matrix-Vector (SpMV) kernel computation hinders the efficiency of iterative algorithms. As modern hardware…
Recently we introduced a class of number representations denoted RN-representations, allowing an un-biased rounding-to-nearest to take place by a simple truncation. In this paper we briefly review the binary fixed-point representation in an…
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…
Floating-point arithmetic performance determines the overall performance of important applications, from graphics to AI. Meeting the IEEE-754 specification for floating-point requires that final results of addition, subtraction,…
There is a growing interest in the use of reduced-precision arithmetic, exacerbated by the recent interest in artificial intelligence, especially with deep learning. Most architectures already provide reduced-precision capabilities (e.g.,…
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…
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…
In todays world, high-power computing applications such as image processing, digital signal processing, graphics, and robotics require enormous computing power. These applications use matrix operations, especially matrix multiplication.…
The precise analysis and accurate measurement of harmonic provides a reliable scientific industrial application. However, the high-performance DSP processor is the important method of electrical harmonic analysis. Hence, in this research…
For scientific computations on a digital computer the set of real number is usually approximated by a finite set F of "floating-point" numbers. We compare the numerical accuracy possible with difference choices of F having approximately the…
Single-precision floating point (FP32) data format, defined by the IEEE 754 standard, is widely employed in scientific computing, signal processing, and deep learning training, where precision is critical. However, FP32 multiplication is…
This paper discusses a simple and effective method for the summation of long sequences of floating point numbers. The method comprises two phases: an accumulation phase where the mantissas of the floating point numbers are added to…
We investigate the question of computational resources (such as stacks and counters) necessary to perform radix conversions. To this end it is shown that no PDA can compute the significand of the best $n$-digit floating point approximation…
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…
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…
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…