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Floating-Point Verification [chapter]

John Harrison
2005 Lecture Notes in Computer Science  
However, in some other respects, 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.  ... 
doi:10.1007/11526841_35 fatcat:lg5ossoiijbblf2ojgwlkqm3p4

Floating Point Verification [chapter]

John Harrison
1998 Theorem Proving with the Real Numbers  
However, in some other respects, 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.  ... 
doi:10.1007/978-1-4471-1591-5_7 fatcat:6owbmyxx6zevjju47bqj72pl3i

Verification of floating-point adders [chapter]

Yirng-An Chen, Randal E. Bryant
1998 Lecture Notes in Computer Science  
The 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.  ... 
doi:10.1007/bfb0028769 fatcat:fzuqaefv4jgkvl25gkix36muwi

Automatic Verification of Floating Point Units

Udo Krautz, Viresh Paruthi, Anand Arunagiri, Sujeet Kumar, Shweta Pujar, Tina Babinsky
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  ... 
doi:10.1145/2593069.2593096 dblp:conf/dac/KrautzPAKPB14 fatcat:2dmb4vqk5rhr7cm67ioe2hlhf4

Formal Verification of Floating-Point Programs

Sylvie Boldo, Jean-Christophe Filliatre
2007 Computer Arithmetic  
This paper introduces a methodology to perform formal 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.  ... 
doi:10.1109/arith.2007.20 dblp:conf/arith/BoldoF07 fatcat:telnp5fv2zahna7hwovoefirk4

Floating-Point Verification Using Theorem Proving [chapter]

John Harrison
2006 Lecture Notes in Computer Science  
This chapter describes our work on formal 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.  ... 
doi:10.1007/11757283_8 fatcat:kz7ckh7iyrglbm4yw3mv4zzd3a

Automating the Verification of Floating-Point Programs [chapter]

Clément Fumex, Claude Marché, Yannick Moy
2017 Lecture Notes in Computer Science  
In the context of deductive program 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.  ... 
doi:10.1007/978-3-319-72308-2_7 fatcat:pj5a5gredzeu7ezxshgnrrjowe

Formal Verification of Floating Point Trigonometric Functions [chapter]

John Harrison
2000 Lecture Notes in Computer Science  
This illustrates the different facets of 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.  ... 
doi:10.1007/3-540-40922-x_14 fatcat:e4fumqurobcsrmgjjgqygwko6m

Multi-Prover Verification of Floating-Point Programs [chapter]

Ali Ayad, Claude Marché
2010 Lecture Notes in Computer Science  
We give a first-order axiomatization of 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.  ... 
doi:10.1007/978-3-642-14203-1_11 fatcat:lje6cjsdvfg47iutx575bq2zh4

Correct Approximation of IEEE 754 Floating-Point Arithmetic for Program Verification [article]

Roberto Bagnara, Abramo Bagnara, Fabio Biselli, Michele Chiari, Roberta Gori
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.  ... 
arXiv:1903.06119v2 fatcat:vcxtvgkebbgixef74lylbazbeq

Formal Verification of the VAMP Floating Point Unit

Christian Jacobi, Christoph Berg
2005 Formal methods in system design  
The 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.  ... 
doi:10.1007/s10703-005-1613-y fatcat:6hk2jqwpgvaonejvisxohro3bi

Polynomial function intervals for floating-point software verification

Jan Duracz, Michal Konečný
2014 Annals of Mathematics and Artificial Intelligence  
The focus of our work is the 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.  ... 
doi:10.1007/s10472-014-9409-7 fatcat:3y3qukebzvcsrpafjwgihilqqm

Formal Verification of the VAMP Floating Point Unit [chapter]

Christoph Berg, Christian Jacobi
2001 Lecture Notes in Computer Science  
The 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.  ... 
doi:10.1007/3-540-44798-9_26 fatcat:pwfqh6djfbfh5hjlq5b2cmqyae

Automatic generation and verification of test-stable floating-point code [article]

Laura Titolo, Mariano Moscato, Cesar A. Muñoz
2020 arXiv   pre-print
The input is a real-valued program written in the Prototype 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)  ... 
arXiv:2001.02981v1 fatcat:556ko7ytyfhdzl2qobelwmss2y

Deductive Verification of Floating-Point Java Programs in KeY [article]

Rosa Abbasi Boroujeni, Jonas Schiffl, Eva Darulova, Mattias Ulbrich, Wolfgang Ahrendt
2021 arXiv   pre-print
In this paper, we present the first 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  ... 
arXiv:2101.08733v1 fatcat:gbpg7i5v2fanje46m7nfj52rli
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