  The IEEE 754-2008 standard recommends the correct rounding of some elementary
functions. This requires to solve the Table Maker's Dilemma which implies a
huge amount of CPU computation time. We consider in this paper accelerating
such computations, namely Lefe'vre algorithm on Graphics Processing Units
(GPUs) which are massively parallel architectures with a partial SIMD execution
(Single Instruction Multiple Data). We first propose an analysis of the
Lef\`evre hard-to-round argument search using the concept of continued
fractions. We then propose a new parallel search algorithm much more efficient
on GPU thanks to its more regular control flow. We also present an efficient
hybrid CPU-GPU deployment of the generation of the polynomial approximations
required in Lef\`evre algorithm. In the end, we manage to obtain overall
speedups up to 53.4x on one GPU over a sequential CPU execution, and up to 7.1x
over a multi-core CPU, which enable a much faster solving of the Table Maker's
Dilemma for the double precision format.
