floating-point satisfiability

Gold definitionUpdated Apr 2, 2026

Definition

Floating-point satisfiability (FPSAT) determines if a system of constraints involving floating-point numbers has a solution. It's crucial for verifying numerical software and hardware, addressing the complexities of finite precision arithmetic.

At a glance

Executive summary

Floating-point satisfiability is about finding solutions to equations and inequalities that use real-world computer numbers (floating-point numbers). StageSAT is a new method that combines optimization with logical solving to find these solutions efficiently, especially for complex problems, by breaking them into stages and using smart search techniques.

TL;DR

It's a method to check if a set of equations using computer's decimal numbers has a valid answer, often used to verify software.

Key points

Core mechanism: Bridges SMT solving with multi-stage numerical optimization (e.g., StageSAT).
Problem solved: Determines if a formula with floating-point constraints has a solution, crucial for verifying numerical correctness.
Who uses it: Researchers in formal verification, program analysis, and computer arithmetic.
Vs main alternative: Unlike traditional SMT solvers that struggle with FP's non-linearity, StageSAT uses optimization and treats arithmetic as a black-box.
Research trend: Growing focus on robust and efficient solvers for floating-point arithmetic in safety-critical systems.

Use cases

Software Verification: Proving the absence of runtime errors (e.g., division by zero, overflow) in numerical libraries and scientific computing code.
Hardware Design Verification: Ensuring the correctness of floating-point units (FPUs) in processors and specialized accelerators.
Numerical Algorithm Analysis: Verifying properties of algorithms that use floating-point numbers, such as stability or convergence under finite precision.
Cyber-Physical Systems: Validating control systems where floating-point computations interact with physical processes.

Also known as

FPSAT, FP-SAT, floating-point constraint solving