A High-Level Formalization of Floating-Point Numbers in PVS
نویسنده
چکیده
We develop a formalization of floating-point numbers in PVS based on a well-known formalization in Coq. We first describe the definitions of all the needed notions, e.g., floating-point number, format, rounding modes, etc. Then, we present an application to polynomial evaluation for elementary function evaluation. The application already existed in Coq, but our formalization shows a clear improvement in the quality of the result due to the automation provided by PVS. Finally, we integrate our formalization into a PVS hardware-level formalization of the IEEE-854 standard previously developed at NASA.
منابع مشابه
Formal verification of a fully IEEE compliant floating point unit
In this thesis we describe the formal verification of a fully IEEE compliant floating point unit (FPU). The hardware is verified on the gate-level against a formalization of the IEEE standard. The verification is performed using the theorem proving system PVS. The FPU supports both single and double precision floating point numbers, normal and denormal numbers, all four IEEE rounding modes, and...
متن کاملFormal Verification of a Theory of IEEE Rounding
We report on the formal verification of a theory of IEEE rounding in the theorem prover PVS. The theory consists of a formalization of the IEEE standard, and notations and theorems facilitating the verification of floating point hardware. In particular, the concepts of -equivalence and round decomposition are formalized, allowing for a subdivision of floating point units into smaller building b...
متن کاملBridging the gap between formal specification and bit-level floating-point arithmetic
Floating-point arithmetic is defined by the IEEE-754 standard and has often been formalized. We propose a new Coq formalization based on the bit-level representation of the standard and we prove strong links between this new formalization and a previous high-level one. In this process, we have defined functions for any rounding mode described by the standard. Our library can now be applied to c...
متن کاملA Parameterized Floating-Point Formalizaton in HOL Light
We present a new, open-source formalization of fixed and floating-point numbers for arbitrary radix and precision that is now part of the HOL Light distribution [10]. We prove correctness and error bounds for the four different rounding modes, and formalize a subset of the IEEE 754 [1] standard by gluing together a set of fixed-point and floating-point numbers to represent the subnormals and no...
متن کاملFormal Verification of the VAMP Floating Point Unit
We report on the formal verification of the floating point unit used in the VAMP processor. The FPU is fully IEEE compliant, and supports denormals and exceptions in hardware. The supported operations are addition, subtraction, multiplication, division, comparison, and conversions. The hardware is verified on the gate level against a formal description of the IEEE standard by means of the theor...
متن کامل