Design of Floating-Point Arithmetic Computational Units for Non Linear Applications

computational science and numerical computing, underpinning a wide range of scientific, engineering, and financial applications. This abstract explores the key aspects of floating-point arithmetic, including its representation, precision limitations, and potential pitfalls. It highlights the trade-off between precision and efficiency in numerical computations and discusses strategies for mitigating errors. We delve into the challenges posed by round-off errors, catastrophic cancellation, and numerical instability, emphasizing their impact on the accuracy of scientific simulations. Additionally, we explore recent advancements in floating-point arithmetic, such as mixed-precision techniques and alternative number representations, aiming to enhance both computational speed and numerical reliability. This abstract serves as an introduction to the complexities and nuances of floating-point arithmetic in computational science, offering valuable insights for researchers and practitioners in the field.