Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 1

Sum of two floating point numbers.

function [𝑥,𝑦]=𝑇𝑤𝑜𝑆𝑢𝑚(𝑎,𝑏)

𝑥=𝑎⊕𝑏

𝑧=𝑥⊖𝑎

𝑦=(𝑎⊖(𝑥⊖𝑧))⊕(𝑏⊖𝑧)