Abstract
Arithmetic expression dags are widely applied in robust geometric computing. In this paper we restructure expression dags by balancing consecutive additions or multiplications. We predict an asymptotic improvement in running time and experimentally confirm the theoretical results. Finally, we discuss some pitfalls of the approach resulting from changes in evaluation order.
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Notes
- 1.
This should more correctly be called “accuracy-driven”, but we use the term “precision-driven” throughout this paper for historical reasons.
- 2.
Real_algebraic usually overestimates the exponent by one, therefore in our tests r is chosen to be smaller than 0.5.
- 3.
This is implemented by inserting dummy nodes up to the next power of two.
- 4.
Or integers divided by a power of two.
- 5.
This behavior was confirmed with both mpfr and leda bigfloats.
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Wilhelm, M. (2017). Balancing Expression Dags for More Efficient Lazy Adaptive Evaluation. In: Blömer, J., Kotsireas, I., Kutsia, T., Simos, D. (eds) Mathematical Aspects of Computer and Information Sciences. MACIS 2017. Lecture Notes in Computer Science(), vol 10693. Springer, Cham. https://doi.org/10.1007/978-3-319-72453-9_2
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