Declarative Numerical Analysis: an Interval Constraint-based Approach

The long term goal of this research is the development of a new approach to scientiic computing in which declarative methods derived from constraint logic programming are used to minimize the avoidable errors that can be made when developing scientiic software. The main approach we will pursue is to explore the beneets and challenges of viewing scientiic computing as interval arithmetic constraint solving. In the previous grant, we developed a powerful interval arithmetic constraint solver, which used the following simple constraint solving strategy: 1. Compile the constraints into an equivalent collection of primitives constraints (similar to compiling arithmetic expressions into three address code) and place them in a queue. 2. Repeatedly remove a primitive constraint, apply the corresponding contraction operator , and then, if any variable intervals were narrowed, enqueue all constraints containing those variables. The solver was designed to work eeciently in a backtracking environment like CLP(BNR) 9, 34, 35], CLP(Intervals))5], or Screamer 43], and so allowed constraints to be added incrementally and supported backtracking to previously saved choice points. All of the primitive contraction operators were implemented assuming only that the underlying arithmetic correctly implemented the IEEE 754 oating point standard 33]. In particular, we re-implemented the elementary functions (exp, log, sin, cos, asin, etc.) in interval arithmetic without using the standard C math library functions. Also, several parallel versions of the solver were implemented and studied. Our proposed research will extend the work in the previous grant in three directions: