This paper presents a comprehensive review of digital floating-point arithmetic algorithms that utilize Taylor series expansion in combination with mantissa-region division techniques, and it further demonstrates their generalization and applicability based on the findings of our research. While the discussion is broad in scope, this paper consolidates and systematizes the authors’ method within a broader contextual discussion, rather than presenting a fully systematic review of the entire state of the art in floating-point arithmetic algorithms. In many scientific computing applications, compact and low-power hardware implementations are essential. To address these requirements, this review presents algorithms specifically designed to operate under such constraints. The focus is placed on efficient floating-point operations—including division, inverse square root, square root, exponentiation, and logarithmic functions—all realized through Taylor series expansion with mantissa region division techniques. Furthermore, the trade-offs are examined in detail, covering factors such as the required numbers of additions, subtractions, and multiplications, along with the look-up table (LUT) size. The study further identifies the environments and application domains where the Taylor series expansion method combined with mantissa-region division is most effective, based on comparisons with various other floating-point computation algorithms and their corresponding hardware implementations. Overall, the review underscores the value of this unified framework in enabling efficient and adaptable floating-point computation across a wide range of hardware-constrained environments.
Wei et al. (Fri,) studied this question.