1. A system for computing narrow bounds on a modal interval polynomial function parameterized by a modal interval function variable U and a control polygon comprising a set of modal interval coefficients B 0 , B 1 ,. .. , B n , the modal interval function variable U and the modal interval coefficients B 0 , B 1 ,. .. , B n being modal intervals delimited by first and second marks of a digital scale, the system comprising: a. a hardware circuit for processing a representation of said modal interval polynomial function; and, b. a modal interval processor for executing a modal interval linear interpolation, said modal interval processor operatively linked to said hardware circuit via a memory addressing unit, said modal interval linear interpolation comprising modal interval arithmetic operations characterized by said modal interval function variable U and select modal interval coefficients of said modal interval coefficients B 0 , B 1 ,. .. , B n , operands of said modal interval arithmetic operations of said modal interval linear interpolation each delimited as a modal interval comprising a quantified set of real numbers.