Polynomial Evaluation
Algorithmic simplification for calculating the value of a polynomial reduces the number of multiplications and additions required per step. Horner’s method rewrites the expression into a nested form, where each coefficient is processed in a sequence of multiply-accumulate operations. This approach is highly efficient for microprocessors that must convert raw sensor counts into physical units using non linear compensation curves.
By minimizing the total operation count, the algorithm reduces both the execution time and the potential for cumulative rounding errors.
Computational Logic
Nested structures transform a standard power based polynomial into a series of linear steps. This reduction is substantial in high speed data acquisition.
Precision Retention
Stability of the calculation improves when using this nested approach because it avoids the large numbers generated by raising values to high powers. Calculating the square or cube of a large raw count can quickly exceed the register width of an embedded processor. This method keeps the intermediate results smaller, which is particularly beneficial when working with fixed point arithmetic.
It maintains a better signal to noise ratio in the final output by preserving more significant bits throughout the process.
Execution Boundary
Suitability of the technique is limited to polynomials where the coefficients are known and fixed during the design phase. While it excels at evaluating a single point, it does not simplify the process of finding the roots or the derivative of the function. For most sensor applications, the calibration curve is determined once and stored in memory, making horner’s method the standard choice for runtime execution.
The primary limit on its use is the degree of the polynomial, as high orders may still introduce latency in low power systems.
