FPbound

FPbound is a term used in numerical analysis to denote a class of methods and tools for bounding errors in floating-point computations. It concerns quantifying the difference between results produced with finite precision and the true real-valued results, typically under the IEEE 754 standard. FPbound emphasizes guarantees about how rounding and limited precision affect numerical outcomes.

The concept emerged from the study of rounding errors and their propagation through arithmetic expressions. Over the 1990s and 2000s, formal methods for deriving and certifying error bounds gained prominence in validated numerics and software verification. FPbound techniques are applied whenever there is a need to certify that computations stay within a specified tolerance.

Technical approaches used in FPbound include interval arithmetic, affine arithmetic, and relational abstractions. Some methods model rounding as bounded perturbations and derive explicit bounds on output errors as functions of input ranges. In practice, FPbound tools may take a program or mathematical expression with known input bounds and compute an upper bound on the result error. They may also generate certificates or proofs of correctness for the reported bounds.

Applications of FPbound concepts span safety-critical software verification, numerical libraries, and optimization where guarantees on results are essential. They are used in domains such as aerospace, automotive control, and scientific computing to ensure reliability under finite-precision arithmetic. Limitations include potential overestimation of bounds, reliance on input range assumptions, and computational complexity for large or highly non-linear programs.

See also floating-point arithmetic, error analysis, interval arithmetic, validated numerics, and formal verification.