Precision-Driven Computation in the Evaluation of Expression-Dags with Common Subexpressions: Problems and Solutions

Internal Versus External Balancing in the Evaluation of Graph-Based Number Types

“…In our default configuration for Real_algebraic we use boost::interval as floating-point filter and mpfr_t as bigfloat data type. Furthermore we always enable topological evaluation, bottom-up separation bound representation and error representation by exponents [9,13]. We call the default strategy without balancing def.…”

Multithreading for the expression-dag-based number type Real_algebraic

“…In 2015 Mörig and Schirra suggested using a topological evaluation order instead of the recursive procedure used in sdag node for the accuracy-driven evaluation [7]. This does not only fix some performance issues, it also enables us to parallelize the evaluation of nodes that are not dependent on each other, i.e., those nodes that are not connected through a directed path.…”

Balancing Expression Dags for More Efficient Lazy Adaptive Evaluation

“…When evaluating a dag-based number type recursively, a slight change in expression order can have an unexpectedly high impact on the evaluation time [7]. Balancing the dag may have a negative impact on the optimal expression order.…”

“…If r > 1 the linear dag and the balanced dag show similar behavior. 2 To avoid extensive recomputations, we can compute a topological order and determine the final accuracy needed at each node before recomputing it [7]. We implement this strategy and compare it with recursive evaluation.…”

“…When evaluating a dag-based number type recursively, a slight change in expression order can have an unexpectedly high impact on the evaluation time [7].…”