Operator Dependant Compensated Algorithms

Compensated algorithms improve the accuracy of a result evaluating a correcting term that compensates the finite precision of the computation. The implementation core of compensated algorithms is the computation of the rounding errors generated by the floating point operators. We focus this operator dependency discussing how to manage and to benefit from floating point arithmetic implemented through a fused multiply and add operator. We consider the compensation of dot product and polynomial evaluation with Horner iteration. In each case we provide theoretical a priori error bounds and numerical experiments to exhibit the best algorithmic choices with respect to accuracy or performance issues.