An advanced data type with irrational numbers to implement time in DEVS simulators

In the Discrete-Event System Specification (DEVS) time variables are Real numbers. This is common to other simulation formalisms for Discrete-Event Simulation (DES). Current simulators for these formalisms approximate time variables using floating-point or rational representations. Neither of them is capable to adequately represent irrational numbers. The representation of these numbers is important, especially for studying systems with geometrical properties. The use of approximations, as floating-point, may silently introduce errors to the causality chain. These errors may produce incorrect simulation trajectories without informing about them. Here, we propose a new data type combining rational data types with computable calculus concepts. This new data type extension provides representation, and operation, with subsets of irrational numbers. The proposed data type only provides four operations (+, -, <;, =), those are sufficient for implementing simulators for DEVS and other DES formalisms. Usage of this data type has no significant complexity penalty for simulation not using irrational numbers.