Improving Floating-Point Numbers: A Lazy Approach to Adaptive Accuracy Refinement for Numerical Computations

Numerical computation using floating-point numbers is prone to accuracy degradation due to round-off errors and cancellation of significant digits. Although multiple-precision arithmetic might alleviate this problem, it is difficult to statically decide the optimal degree of precision for each operation in a program. This paper presents a solution to this problem: the partial results in floating-point representations are incrementally improved using adaptive control. This process of adaptive accuracy refinement is implemented using lazy lists, each one containing a sequence of floating-point numbers with gradually improving accuracies. The computation process is driven by the propagation of demand for more accurate results. The concept of this improving floating-point number (IFN) mechanism was experimentally implemented in two ways: as a Haskell library and as a pure C library. Despite the simple approach, the results for numerical problems demonstrated the effectiveness of this mechanism.