Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 10

Addition of a double-double number and a double-double number.

function [𝑟ℎ,𝑟𝑙]=𝑎𝑑𝑑_𝑑𝑑_𝑑𝑑(𝑎ℎ,𝑎𝑙,𝑏ℎ,𝑏𝑙)

[𝑠ℎ,𝑠𝑙]=𝑇𝑤𝑜𝑆𝑢𝑚(𝑎ℎ,𝑏ℎ)

[𝑡ℎ,𝑡𝑙]=𝑇𝑤𝑜𝑆𝑢𝑚(𝑎𝑙,𝑏𝑙)

𝑠𝑙=𝑠𝑙⊕𝑡ℎ

𝑡ℎ=𝑠ℎ⊕𝑠𝑙

𝑠𝑙=𝑠𝑙⊖(𝑡ℎ⊖𝑠ℎ)

𝑡𝑙=𝑡𝑙⊕𝑠𝑙

[𝑟ℎ,𝑟𝑙]=𝐹𝑎𝑠𝑡𝑇𝑤𝑜𝑆𝑢𝑚(𝑡ℎ,𝑡𝑙)