Verification of IEEE compliant subtractive division algorithms

Miner, Paul S.; Leathrum, James F.

doi:10.1007/bfb0031800

Cited by 25 publications

(13 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This poly is the result of cancelling the two polys in the a·b pot. 10 Upon adding it and canceling the polys in the b pot (executing steps 2 and 1 again), we get the contradiction 0 < −1 and our lemma is proved.…”

Section: An Examplementioning

confidence: 70%

See 1 more Smart Citation

Linear and Nonlinear Arithmetic in ACL2

Hunt

Krug

Moore

2003

Lecture Notes in Computer Science

View full text Add to dashboard Cite

Abstract. As of version 2.7, the ACL2 theorem prover has been extended to automatically verify sets of polynomial inequalities that include nonlinear relationships. In this paper we describe our mechanization of linear and nonlinear arithmetic in ACL2. The nonlinear arithmetic procedure operates in cooperation with the pre-existing ACL2 linear arithmetic decision procedure. It extends what can be automatically verified with ACL2, thereby eliminating the need for certain types of rules in ACL2's database while simultaneously increasing the performance of the ACL2 system when verifying arithmetic conjectures. The resulting system lessens the human effort required to construct a large arithmetic proof by reducing the number of intermediate lemmas that must be proven to verify a desired theorem.

show abstract

Section: An Examplementioning

confidence: 70%

“…Great progress has been made as is illustrated by the many substantial proofs recently completed in PVS, HOL, and ACL2 [10,5,13]. The existing state-of-the-art is, however, not sufficient.…”

Section: Related Work and Plan Of The Papermentioning

confidence: 99%

Linear and Nonlinear Arithmetic in ACL2

Hunt

Krug

Moore

2003

Lecture Notes in Computer Science

View full text Add to dashboard Cite

show abstract

“…His work was one of the earliest on the formalization of floating-point standards using theorem proving. His formal specification was then used by Miner and Leathrum [30] to verify in PVS a general class of IEEE compliant subtractive division algorithms.…”

Section: Related Workmentioning

confidence: 99%

Formalization of Fixed-Point Arithmetic in HOL

Akbarpour

Tahar

Dekdouk

2005

Form Method Syst Des

View full text Add to dashboard Cite

Abstract. This paper addresses the formalization in higher-order logic of fixed-point arithmetic. We encoded the fixed-point number system and specified the different quantization modes in fixed-point arithmetic such as the directed and even quantization modes. We also considered the formalization of exceptions detection and their handling like overflow and invalid operation. An error analysis is then performed to check the correctness of the quantized result after carrying out basic arithmetic operations, such as addition, subtraction, multiplication and division against their mathematical counterparts. Finally, we showed by an example how this formalization can be used to enable the verification of the transition from floating-point to fixed-point algorithmic level in the signal processing design flow.

show abstract

“…Theorem provers have long been used to mechanically check the correctness of floating point algorithms with PVS [19,26], HOL [16], or ACL2 [31], and one specification has been motivated by avionic application [4]. Guaranteeing the completeness of a specification with respect to a text in a natural language is probably beyond the scope of formal proof.…”

Section: Fallacies and Pitfallsmentioning

confidence: 99%

Properties of two’s complement floating point notations

Boldo

Daumas

2004

STTT

View full text Add to dashboard Cite

Abstract. Few designs, mostly those of Texas Instruments, continue to use two's complement floating point units. Such units are simpler to build and to validate, but they do not comply to the dominant IEEE standard for floating point arithmetic. We compare some properties of the two systems in this text. Some features are lost, but others remain unchanged. One strong example is the case of Sterbenz's theorem and our recent extension. We show in the paper that the theorem and its extension hold for the two's complement architecture. Still, users should ensure that results are large enough on circuits that do not implement gradual underflow. Theorems have been proven and validated using the Coq automatic proof checker.

show abstract

Verification of IEEE compliant subtractive division algorithms

Cited by 25 publications

References 9 publications

Linear and Nonlinear Arithmetic in ACL2

Linear and Nonlinear Arithmetic in ACL2

Formalization of Fixed-Point Arithmetic in HOL

Properties of two’s complement floating point notations

Contact Info

Product

Resources

About