System and method for efficient even polynomial evaluation using transformation-enhanced fused multiply-add operations

A computer-implemented method for evaluating even polynomials in a hardware computing system, comprising:

• performing a degree-2n even polynomial evaluation completed using no more than n FMA operations by:
• acquiring, by a scheduling controller from a configuration memory, a transformation constant (α) and a plurality of restructured polynomial coefficients optimized for floating-point multiply-add (FMA) operations;
• receiving an input value at a first FMA unit from a plurality of FMA units, the first FMA unit having dedicated multiplication circuitry and addition circuitry;
• configuring the first FMA unit to compute an intermediate processing variable (y) by executing a multiply-add operation that utilizes both the multiplication circuitry and the addition circuitry in a single hardware operation, wherein the transformation constant (α) is added during computation of the intermediate processing variable (y=x2+α) where x is an input value of the first FMA;
• allocating, by the scheduling controller, at least two additional FMA units from the plurality of FMA units to execute parallel FMA operations using the intermediate processing variable and independent inputs to generate intermediate polynomial terms, wherein the transformation constant (α) restructures computational dependencies to enable parallel calculation of the intermediate polynomial terms;
• and
• performing additional FMA operations through the plurality of FMA units to process the intermediate polynomial terms using the plurality of restructured polynomial coefficients and complete the polynomial evaluation.