Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 12

Multiplication of a double-double number by a double-double number.

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

[𝑡ℎ,𝑡𝑙]=𝑇𝑤𝑜𝑃𝑟𝑜𝑑(𝑎ℎ,𝑏ℎ)

𝑡𝑙=(𝑎ℎ⊗𝑏𝑙)⊕(𝑎𝑙⊗𝑏ℎ)⊕𝑡𝑙

[𝑟ℎ,𝑟𝑙]=𝐹𝑎𝑠𝑡𝑇𝑤𝑜𝑆𝑢𝑚(𝑡ℎ,𝑡𝑙)