Accurate Evaluation of Polynomials in Legendre Basis

Algorithm 14

Division of a double-double number by a double-double number.

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

𝑞1=𝑎ℎ⊘𝑏ℎ

[𝑡ℎ1,𝑡𝑙1]=𝑝𝑟𝑜𝑑_𝑑𝑑_𝑑(𝑏ℎ,𝑏𝑙,𝑞1)

[𝑡ℎ2,𝑡𝑙2]=𝑎𝑑𝑑_𝑑𝑑_𝑑𝑑(𝑎ℎ,𝑎𝑙,−𝑡ℎ1,−𝑡𝑙1)

𝑞2=𝑡ℎ2⊘𝑏ℎ

[𝑡ℎ1,𝑡𝑙1]=𝑝𝑟𝑜𝑑_𝑑𝑑_𝑑(𝑏ℎ,𝑏𝑙,𝑞2)

[𝑡ℎ2,𝑡𝑙2]=𝑎𝑑𝑑_𝑑𝑑_𝑑𝑑(𝑡ℎ2,𝑡𝑙2,−𝑡ℎ1,−𝑡𝑙1)

𝑞3=𝑡ℎ2⊘𝑏ℎ

[𝑞1,𝑞2]=𝐹𝑎𝑠𝑡𝑇𝑤𝑜𝑆𝑢𝑚(𝑞1,𝑞2)

[𝑟ℎ,𝑟𝑙]=𝑎𝑑𝑑_𝑑𝑑_𝑑(𝑞1,𝑞2,𝑞3)