A Review of Floating-Point Arithmetic Algorithms Using Taylor Series Expansion and Mantissa Region Division Techniques

This paper reviews digital floating-point arithmetic algorithms that employ Taylor series expansion combined with mantissa region division techniques, drawing upon the results of our research. 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 expansions. Furthermore, the paper examines the trade-offs involved, such as the number of additions, subtractions, and multiplications, as well as the hardware cost associated with Look-Up Table (LUT) size. These factors are analyzed to identify the most suitable algorithms for engineering applications and to facilitate their practical implementation.