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Floating-Point Verification
[chapter]

2005
*
Lecture Notes in Computer Science
*

However, in some other respects,

doi:10.1007/11526841_35
fatcat:lg5ossoiijbblf2ojgwlkqm3p4
*floating*-*point*operations present a difficult challenge for formal*verification*. ... There are many theorem proving programs, 1 and quite a few have been applied to*floating*-*point**verification*, including at least ACL2, Coq, HOL Light and PVS. ...##
###
Floating Point Verification
[chapter]

1998
*
Theorem Proving with the Real Numbers
*

However, in some other respects,

doi:10.1007/978-1-4471-1591-5_7
fatcat:6owbmyxx6zevjju47bqj72pl3i
*floating*-*point*operations present a difficult challenge for formal*verification*. ... There are many theorem proving programs, 1 and quite a few have been applied to*floating*-*point**verification*, including at least ACL2, Coq, HOL Light and PVS. ...##
###
Verification of floating-point adders
[chapter]

1998
*
Lecture Notes in Computer Science
*

The

doi:10.1007/bfb0028769
fatcat:fzuqaefv4jgkvl25gkix36muwi
*floating*-*point*(FP) division bug in Intel's Pentium processor and the overflow flag erratum of the FIST instruction in Intel's Pentium Pro and Pentium II processor have demonstrated the importance and ... For each of FP adders, the*verification*task finished in 2 CPU hours on a Sun UltraSPARC-II server. ...*Floating*-*Point*Adders Let us consider the representation of FP numbers by IEEE standard 754. ...##
###
Automatic Verification of Floating Point Units

2014
*
Proceedings of the The 51st Annual Design Automation Conference on Design Automation Conference - DAC '14
*

*Floating*

*Point*Units (FPUs) pose a singular challenge for traditional

*verification*methods, such as coverage driven simulation, given the large and complex data paths and intricate control structures which ... In our experience this is a one of a kind approach to perform automated end-to-end

*verification*of FPUs. ... In experiment 3 we present results for a 64bit decimal

*floating*

*point*compare instruction that followed a 128bit decimal

*floating*

*point*add in 3a and a 64bit binary

*floating*

*point*convert to decimal in ...

##
###
Formal Verification of Floating-Point Programs

2007
*
Computer Arithmetic
*

This paper introduces a methodology to perform formal

doi:10.1109/arith.2007.20
dblp:conf/arith/BoldoF07
fatcat:telnp5fv2zahna7hwovoefirk4
*verification*of*floating*-*point*C programs. ... It extends an existing tool for the*verification*of C programs, Caduceus, with new annotations specific to*floating*-*point*arithmetic. ... Conclusions and perspectives We have presented a formal*verification*framework for*floating*-*point*programs. ...##
###
Floating-Point Verification Using Theorem Proving
[chapter]

2006
*
Lecture Notes in Computer Science
*

This chapter describes our work on formal

doi:10.1007/11757283_8
fatcat:kz7ckh7iyrglbm4yw3mv4zzd3a
*verification*of*floating*-*point*algorithms using the HOL Light theorem prover. let th6 = REAL_ARITH 'abs(c -a) < e ∧ abs(b) <= d =⇒ abs((a + b) -c) < d + e';; ...*Floating*-*point*algorithms are in some ways an especially natural and appealing target for formal*verification*. ... In some other respects though,*floating*-*point*operations present a difficult challenge for formal*verification*. ...##
###
Automating the Verification of Floating-Point Programs
[chapter]

2017
*
Lecture Notes in Computer Science
*

In the context of deductive program

doi:10.1007/978-3-319-72308-2_7
fatcat:pj5a5gredzeu7ezxshgnrrjowe
*verification*, handling*floating*-*point*computations is challenging. ... One of these strategies is based on the native support for*floating*-*point*arithmetic recently added in the SMT-LIB standard. ... Conclusions and Perspectives Our approach for automated*verification*of*floating*-*point*programs relies on a generic theory, written in Why3's specification language, to model FP arithmetic. ...##
###
Formal Verification of Floating Point Trigonometric Functions
[chapter]

2000
*
Lecture Notes in Computer Science
*

This illustrates the different facets of

doi:10.1007/3-540-40922-x_14
fatcat:e4fumqurobcsrmgjjgqygwko6m
*verification*in this field, covering both pure mathematics and the detailed analysis of*floating**point*rounding. ... We have formal verified a number of algorithms for evaluating transcendental functions in double-extended precision*floating**point*arithmetic in the Intel® IA-64 architecture. ... Having done that, we can proceed with the*verification*of the actual computation of the reduced argument in*floating**point*arithmetic. ...##
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Multi-Prover Verification of Floating-Point Programs
[chapter]

2010
*
Lecture Notes in Computer Science
*

We give a first-order axiomatization of

doi:10.1007/978-3-642-14203-1_11
fatcat:lje6cjsdvfg47iutx575bq2zh4
*floating*-*point*operations which allows to reduce*verification*to checking the validity of logic formulas, in a suitable form for a large class of provers including ... 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. ... The IEEE-754 Standard for*Floating*-*Point*Arithmetic The IEEE-754 standard [1] defines an expected behavior of FP computations. ...##
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Correct Approximation of IEEE 754 Floating-Point Arithmetic for Program Verification
[article]

2021
*
arXiv
*
pre-print

*Verification*of programs using

*floating*-

*point*arithmetic is challenging on several accounts. ... This is an important slab for paving the way to formal

*verification*of programs that use

*floating*-

*point*arithmetics. ...

*Floating*-

*Point*Program

*Verification*Several program analyses for automatic detection of

*floating*-

*point*exceptions were proposed in the literature. ...

##
###
Formal Verification of the VAMP Floating Point Unit

2005
*
Formal methods in system design
*

The

doi:10.1007/s10703-005-1613-y
fatcat:6hk2jqwpgvaonejvisxohro3bi
*verification*of the combinatorial*floating**point*circuits is complete. We are currently working on the*verification*of the FPU pipeline control. ... The*verification*of*floating**point*algorithms and hardware using formal methods has received considerable attention over the last years. ... It can perform*floating**point*addition, subtraction, multiplication, division, comparison, conversion between both*floating**point*formats, and conversion between*floating**point*numbers and integers. ...##
###
Polynomial function intervals for floating-point software verification

2014
*
Annals of Mathematics and Artificial Intelligence
*

The focus of our work is the

doi:10.1007/s10472-014-9409-7
fatcat:3y3qukebzvcsrpafjwgihilqqm
*verification*of tight functional properties of numerical programs, such as showing that a*floating*-*point*implementation of Riemann integration computes a close approximation ... To support our claim of expressivity, we outline the*verification*of four example programs, including the integration example mentioned earlier. ... While PolyPaver can be applied in various contexts, it was developed with*verification*of*floating*-*point*programs in mind. ...##
###
Formal Verification of the VAMP Floating Point Unit
[chapter]

2001
*
Lecture Notes in Computer Science
*

The

doi:10.1007/3-540-44798-9_26
fatcat:pwfqh6djfbfh5hjlq5b2cmqyae
*verification*of the combinatorial*floating**point*circuits is complete. We are currently working on the*verification*of the FPU pipeline control. ... The*verification*of*floating**point*algorithms and hardware using formal methods has received considerable attention over the last years. ... It can perform*floating**point*addition, subtraction, multiplication, division, comparison, conversion between both*floating**point*formats, and conversion between*floating**point*numbers and integers. ...##
###
Automatic generation and verification of test-stable floating-point code
[article]

2020
*
arXiv
*
pre-print

The input is a real-valued program written in the Prototype

arXiv:2001.02981v1
fatcat:556ko7ytyfhdzl2qobelwmss2y
*Verification*System (PVS) specification language and the output is a transformed*floating*-*point*C program annotated with ANSI/ISO C Specification ... These contracts relate the*floating*-*point*program to its functional specification in real arithmetic. ... sound estimations of the round-off error that may occur in a*floating*-*point*program, -Frama-C [37] , a collaborative tool suite for the analysis of C code, and the Prototype*Verification*System (PVS) ...##
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Deductive Verification of Floating-Point Java Programs in KeY
[article]

2021
*
arXiv
*
pre-print

In this paper, we present the first

arXiv:2101.08733v1
fatcat:gbpg7i5v2fanje46m7nfj52rli
*floating*-*point*support in a deductive*verification*tool for the Java programming language. ... Deductive*verification*has been successful in verifying interesting properties of real-world programs. One notable gap is the limited support for*floating*-*point*reasoning. ... If we reason about*floating*-*point*problems in isolation, they are not needed, but if we want to consider Java*verification*more holistically with questions combining aspects of heap and*floating**point*...
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