Type System Support for Floating-Point Computation

Floating-point arithmetic is often seen as untrustworthy. We show how manipulating precisions according to the following rules of thumb enhances the reliability of and removes surprises from calculations: • Store data narrowly, • compute intermediates widely, and • derive properties widely. Further, we describe a typing system for floating point that both supports and is supported by these rules. A single type is established for all intermediate computations. The type describes a precision at least as wide as all inputs to and results from the computation. Picking a single type provides benefits to users, compilers, and interpreters. The type system also extends cleanly to encompass intervals and higher precisions.