Evaluation Method
Mathematical method for the efficient evaluation of high order algebraic expressions reduces the number of multiplications required to compute a value. A horner scheme polynomial rearranges the standard power series into a nested form of additions and multiplications. This structure is particularly effective for calculating sensor compensation curves in embedded firmware where resources are limited and precision is required.
Computational Efficiency
Nested multiplication requires only N additions and N multiplications for a polynomial of degree N. Using the horner scheme polynomial decreases the instruction count compared to calculating powers of the input variable individually. Reduced processor load allows for more frequent updates of the output signal.
Numerical Precision
Rounding errors are minimized because the method avoids the intermediate calculation of very large or very small exponents. Implementation of a horner scheme polynomial maintains better stability in the presence of limited bit depth. Calculations proceed from the highest coefficient down to the constant term.
Implementation Strategy
Firmware developers use this technique to translate raw ADC counts into physical units like temperature or pressure. A horner scheme polynomial provides a balance between memory usage and execution speed. Correctness is verified by comparing the results against a reference table of values.
