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29
PVS: Combining Specification, Proof Checking, and Model Checking
, 1996
"... rem Proving and Typechecking The PVS specification language is based on classical, simply typed higherorder logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks for simp ..."
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Cited by 207 (4 self)
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rem Proving and Typechecking The PVS specification language is based on classical, simply typed higherorder logic, but the type system has been augmented with subtypes and dependent types. Though typechecking is undecidable for the PVS type system, the PVS typechecker automatically checks for simple type correctness and generates proof obligations corresponding to predicate subtypes. These proof obligations can be discharged through the use of the PVS proof checker. PVS also has parametric theories so that it is possible to capture, say, the notion of sorting with respect to arbitrary sizes, types, and ordering relations. By exploiting subtyping, dependent typing, and parametric theories, researchers at NASA Langley Research Center and SRI have developed a very general bitvector library. Paul Miner at NASA ? The development of PVS was funded by SRI International through IR&D funds. Various applications and customizations have been funded by NSF Grant CCR9300
ACL2 Theorems about Commercial Microprocessors
, 1996
"... ACL2 is a mechanized mathematical logic intended for use in specifying and proving properties of computing machines. In two independent projects, industrial engineers have collaborated with researchers at Computational Logic, Inc. (CLI), to use ACL2 to model and prove properties of stateoftheart ..."
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Cited by 68 (14 self)
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ACL2 is a mechanized mathematical logic intended for use in specifying and proving properties of computing machines. In two independent projects, industrial engineers have collaborated with researchers at Computational Logic, Inc. (CLI), to use ACL2 to model and prove properties of stateoftheart commercial microprocessors prior to fabrication. In the first project, Motorola, Inc., and CLI collaborated to specify Motorola's complex arithmetic processor (CAP), a singlechip, digital signal processor (DSP) optimized for communications signal processing. Using the specification, we proved the correctness of several CAP microcode programs. The second industrial collaboration involving ACL2 was between Advanced Micro Devices, Inc. (AMD) and CLI. In this work we proved the correctness of the kernel of the floatingpoint division operation on AMD's first Pentiumclass microprocessor, the AMD5K 86. In this paper, we discuss ACL2 and these industrial applications, with particular attention ...
A MachineChecked Theory of Floating Point Arithmetic
, 1999
"... . Intel is applying formal verification to various pieces of mathematical software used in Merced, the first implementation of the new IA64 architecture. This paper discusses the development of a generic floating point library giving definitions of the fundamental terms and containing formal pr ..."
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Cited by 31 (5 self)
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. Intel is applying formal verification to various pieces of mathematical software used in Merced, the first implementation of the new IA64 architecture. This paper discusses the development of a generic floating point library giving definitions of the fundamental terms and containing formal proofs of important lemmas. We also briefly describe how this has been used in the verification effort so far. 1 Introduction IA64 is a new 64bit computer architecture jointly developed by HewlettPackard and Intel, and the forthcoming Merced chip from Intel will be its first silicon implementation. To avoid some of the limitations of traditional architectures, IA64 incorporates a unique combination of features, including an instruction format encoding parallelism explicitly, instruction predication, and speculative /advanced loads [4]. Nevertheless, it also offers full upwardscompatibility with IA32 (x86) code. 1 IA64 incorporates a number of floating point operations, the centerpi...
A Mechanically Checked Proof of the Correctness of the Kernel of the AMD5K86 FloatingPoint Division Algorithm
 IEEE Transactions on Computers
, 1996
"... We describe a mechanically checked proof of the correctness of the kernel of the floating point division algorithm used on the AMD5K 86 microprocessor. The kernel is a nonrestoring division algorithm that computes the floating point quotient of two double extended precision floating point numbers, ..."
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Cited by 30 (11 self)
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We describe a mechanically checked proof of the correctness of the kernel of the floating point division algorithm used on the AMD5K 86 microprocessor. The kernel is a nonrestoring division algorithm that computes the floating point quotient of two double extended precision floating point numbers, p and d (d 6= 0), with respect to a rounding mode, mode. The algorithm is defined in terms of floating point addition and multiplication. First, two NewtonRaphson iterations are used to compute a floating point approximation of the reciprocal of d. The result is used to compute four floating point quotient digits in the 24,,17 format (24 bits of precision and 17 bit exponents) which are then summed using appropriate rounding modes. We prove that if p and d are 64,,15 (possibly denormal) floating point numbers, d 6= 0 and mode specifies one of six rounding procedures and a desired precision 0 ! n 64, then the output of the algorithm is p=d rounded according to mode. We prove that every int...
Specification of the IEEE854 FloatingPoint Standard in HOL and PVS
, 1995
"... The IEEE854 Standard for radixindependent floatingpoint arithmetic has been partially defined within two mechanical verification systems. We present the specification of key parts of the standard in both HOL and PVS. This effort to formalize IEEE854 has given the opportunity to compare the st ..."
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Cited by 24 (1 self)
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The IEEE854 Standard for radixindependent floatingpoint arithmetic has been partially defined within two mechanical verification systems. We present the specification of key parts of the standard in both HOL and PVS. This effort to formalize IEEE854 has given the opportunity to compare the styles imposed by the two verification systems on the specification.
Putting it all together — Formal Verification of the VAMP
 International Journal on Software Tools for Technology Transfer (STTT
"... Abstract. In the VAMP (verified architecture microprocessor) project we have designed, functionally verified, and synthesized a processor with full DLX instruction set, delayed branch, Tomasulo scheduler, maskable nested precise interrupts, pipelined fully IEEE compatible dual precision floating poi ..."
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Cited by 21 (2 self)
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Abstract. In the VAMP (verified architecture microprocessor) project we have designed, functionally verified, and synthesized a processor with full DLX instruction set, delayed branch, Tomasulo scheduler, maskable nested precise interrupts, pipelined fully IEEE compatible dual precision floating point unit with variable latency, and separate instruction and data caches. The verification has been carried out in the theorem proving system PVS. The processor has been implemented on a Xilinx FPGA. 1
MultiProver Verification of FloatingPoint Programs ⋆
"... Abstract. In the context of deductive program verification, supporting floatingpoint computations is tricky. We propose an expressive language to formally specify behavioral properties of such programs. We give a firstorder axiomatization of floatingpoint operations which allows to reduce verifica ..."
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Cited by 14 (3 self)
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Abstract. In the context of deductive program verification, supporting floatingpoint computations is tricky. We propose an expressive language to formally specify behavioral properties of such programs. We give a firstorder axiomatization of floatingpoint operations which allows to reduce verification to checking the validity of logic formulas, in a suitable form for a large class of provers including SMT solvers and interactive proof assistants. Experiments using the FramaC platform for static analysis of C code are presented. 1
Automatic formal verification of fusedmultiplyadd FPUs
 in DATE
, 2005
"... In this paper we describe a fullyautomated methodology for formal verification of fusedmultiplyadd floating point units (FPUs). Our methodology verifies an implementation FPU against a simple reference model derived from the processor’s architectural specification, which may include all aspects o ..."
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Cited by 13 (5 self)
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In this paper we describe a fullyautomated methodology for formal verification of fusedmultiplyadd floating point units (FPUs). Our methodology verifies an implementation FPU against a simple reference model derived from the processor’s architectural specification, which may include all aspects of the IEEE specification including denormal operands and exceptions. Our strategy uses a combination of BDD and SATbased symbolic simulation. To make this verification task tractable, we use a combination of casesplitting, multiplier isolation, and automatic model reduction techniques. The casesplitting is defined only in terms of the reference model, which makes this approach easily portable to new designs. The methodology is directly applicable to multiGHz industrial implementation models (e.g., HDL or gatelevel circuit representations) that contain all details of the highperformance transistorlevel model, such as aggressive pipelining, clocking, etc. Experimental results are provided to demonstrate the computational efficiency of this approach. 1
Formal Verification of the VAMP Floating Point Unit
 In CHARME 2001, volume 2144 of LNCS
, 2001
"... 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 v ..."
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Cited by 12 (6 self)
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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 theorem prover PVS.
Modular Verification of SRT Division
, 1996
"... . We describe a formal specification and verification in PVS for the general theory of SRT division, and for the hardware design of a specific implementation. The specification demonstrates how attributes of the PVS language (in particular, predicate subtypes) allow the general theory to be deve ..."
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Cited by 11 (1 self)
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. We describe a formal specification and verification in PVS for the general theory of SRT division, and for the hardware design of a specific implementation. The specification demonstrates how attributes of the PVS language (in particular, predicate subtypes) allow the general theory to be developed in a readable manner that is similar to textbook presentations, while the PVS table construct allows direct specification of the implementation's quotient lookup table. Verification of the derivations in the SRT theory and for the data path and lookup table of the implementation are highly automated and performed for arbitrary, but finite precision; in addition, the theory is verified for general radix, while the implementation is specialized to radix 4. The effectiveness of the automation derives from PVS's tight integration of rewriting with decision procedures for equality, linear arithmetic over integers and rationals, and propositional logic. This example demonstrates t...