The Harmonized Parabolic Synthesis with Squaring Shrunk Method for Inverse Square Root

In linear algebra, inverse square root is highly convenient for normalizing a vector. A normalized vector is crucial in calculations involving reflections, such as in 3D graphics rendering. An increase in computation speed for these tasks translates into faster rendering or higher-precision rendering. This paper adopts the Harmonized Parabolic Synthesis method(HPS) and introduces the vertex form of the parabolic equation to implement the inverse square root on FPGA. Through precision analysis and hardware implement results, it has been demonstrated that this approach reduces hardware resources compared to traditional HPS, while also improving precision and computation speed compared to the Newton-Raphson method.