A Fixed-Point Binary Decomposition Method for Efficient Exponential Approximation in Embedded Systems
Oscar Jackson · 2025
In embedded electronics, low-cost microcontrollers often lack floating point units and have limited arithmetic capability, making traditional transcendental function evaluation computationally expensive [1, 2]. Common methods for approximating the exponential function-such as Taylor series, Padé approximants, or CORDIC-based sinh/cosh identities-typically require floating point operations, divisions, and multiple iterative steps, which can be impractical on constrained hardware [3, 4, 5]. This work introduces a novel algorithm for computing e x using fixed-point arithmetic, binary decomposition of the exponent, and a precomputed table of e 2−i constants. The method eliminates floating point and division operations entirely, offering fast, constant-time execution while maintaining acceptable accuracy across a practical input range. This approach is particularly suited to low-power embedded applications requiring efficient calibration, control, or inference logic [2, 6].