Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 13

Division of a double number by a double number.

function [𝑟ℎ,𝑟𝑙]=𝑑𝑖𝑣_𝑑_𝑑(𝑎,𝑏)

𝑞ℎ=𝑎⊘𝑏

[𝑡ℎ1,𝑡𝑙1]=𝑇𝑤𝑜𝑃𝑟𝑜𝑑(𝑞ℎ,𝑏)

[𝑡ℎ2,𝑡𝑙2]=𝑇𝑤𝑜𝑆𝑢𝑚(𝑎,−𝑡ℎ1)

𝑞𝑙=(𝑡ℎ2⊕𝑡𝑙2⊖𝑡𝑙1)⊘𝑏

[𝑟ℎ,𝑟𝑙]=𝐹𝑎𝑠𝑡𝑇𝑤𝑜𝑆𝑢𝑚(𝑞ℎ,𝑞𝑙)