Static Analysis for Efficient Affine Arithmetic on GPUs
Bryan Chan · UWSpace (University of Waterloo) · 2008
I hereby declare that I am the sole author of this thesis. This is a true copy of the thesis, including any required final revisions, as accepted by my examiners. I understand that my thesis may be made electronically available to the public. Bryan Chan ii Range arithmetic is a way of calculating with variables that hold ranges of real values. This ability to manage uncertainty during computation has many applications. Examples in graphics include rendering and surface modeling, and there are more general applications like global optimization and solving systems of nonlinear equations. This thesis focuses on affine arithmetic, one kind of range arithmetic. The main drawbacks of affine arithmetic are that it taxes processors with heavy use of floating point arithmetic and uses expensive sparse vectors to represent noise symbols. Stream processors like graphics processing units (GPUs) excel at intense computation, since they were originally designed for high throughput media applications. Heavy control flow and