Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 3

Product of two floating point numbers.

function [𝑥,𝑦]=𝑇𝑤𝑜𝑃𝑟𝑜𝑑(𝑎,𝑏)

𝑥=𝑎⊗𝑏

[𝑎ℎ,𝑎𝑙]=𝑆𝑝𝑙𝑖𝑡(𝑎)

[𝑏ℎ,𝑏𝑙]=𝑆𝑝𝑙𝑖𝑡(𝑏)

𝑦=𝑎𝑙⊗𝑏𝑙⊖(((𝑥⊖𝑎ℎ⊗𝑏ℎ)⊖𝑎𝑙⊗𝑏ℎ)⊖𝑎ℎ⊗𝑏𝑙)