Writing parallel versions for shared memory multi-core computers with Ada tasks requires minimal modifications of the original source code. For pleasingly parallel computations we experienced almost optimal speedups. If we can afford to spend the same amount of time as one core, then we can ask how much better (e.g.: how much more accurate) we can solve a problem with p cores. This leads to the notion to "quality up". Similar to speedup factors, we can compute "quality up" factors.

In this talk we report on our coding efforts to write multi-core versions of the path trackers in PHCpack, a free and open source software package to solve polynomial systems. We started investigating the use of multi-threading to compensate for the overhead of double double and quad double arithmetic.