Approximate Floating-Point Operations with Integer Units by Processing in the Logarithmic Domain

Floating-point numbers represented using a hidden one can readily be approximately converted to the logarithmic domain using Mitchell's approximation. Once in the logarithmic domain, several arithmetic operations including multiplication, division, and square-root can be easily computed using the integer arithmetic unit. This has earlier been used in fast reciprocal square-root algorithms, sometimes referred to as magic number algorithms. The proposed approximate operations are realized by performing an integer operation using an integer unit on floating-point data and adding an integer constant to obtain the approximate floating-point result. In this work, we derive easy to use equations and constants for multiple floating-point formats and operations.