## Floating-point verification (1995)

Venue: | International Journal Of Man-Machine Studies |

Citations: | 3 - 0 self |

### BibTeX

@INPROCEEDINGS{Harrison95floating-pointverification,

author = {John Harrison},

title = {Floating-point verification},

booktitle = {International Journal Of Man-Machine Studies},

year = {1995},

pages = {342--344},

publisher = {Springer Verlag}

}

### OpenURL

### Abstract

Abstract: This paper overviews the application of formal verification techniques to hardware in general, and to floating-point hardware in particular. A specific challenge is to connect the usual mathematical view of continuous arithmetic operations with the discrete world, in a credible and verifiable way.

### Citations

2921 | Graph-based algorithms for Boolean function manipulation
- Bryant
- 1986
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Citation Context ...cation, significant success has been achieved using highly automated techniques, usually based on a Boolean model of the state of the system.sFor example, efficient algorithms for propositional logic =-=[1, 5, 22]-=- and their aggressively efficient implementation [16] have made possible a variety of techniques ranging from simple Boolean equivalence checking of combinational circuits to more advanced model check... |

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- 2001
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Citation Context ...automated techniques, usually based on a Boolean model of the state of the system.sFor example, efficient algorithms for propositional logic [1, 5, 22] and their aggressively efficient implementation =-=[16]-=- have made possible a variety of techniques ranging from simple Boolean equivalence checking of combinational circuits to more advanced model checking of sequential systems [3, 18, 2, 21]. But it is l... |

794 |
Design and Synthesis of Synchronization Skeletons Using Branching-Time Temporal Logic
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- 1982
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Citation Context ...ficient implementation [16] have made possible a variety of techniques ranging from simple Boolean equivalence checking of combinational circuits to more advanced model checking of sequential systems =-=[3, 18, 2, 21]-=-. But it is less easy to verify non-trivial floating-point arithmetic operations using such techniques. The natural specifications, including the IEEE Standard, are based on real numbers, not bit-stri... |

739 |
A Machine Program for Theorem Proving
- Davis, Logemann, et al.
- 1962
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Citation Context ...cation, significant success has been achieved using highly automated techniques, usually based on a Boolean model of the state of the system.sFor example, efficient algorithms for propositional logic =-=[1, 5, 22]-=- and their aggressively efficient implementation [16] have made possible a variety of techniques ranging from simple Boolean equivalence checking of combinational circuits to more advanced model check... |

573 | Symbolic model checking: 10 20 states and beyond
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- 1990
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Citation Context ...ficient implementation [16] have made possible a variety of techniques ranging from simple Boolean equivalence checking of combinational circuits to more advanced model checking of sequential systems =-=[3, 18, 2, 21]-=-. But it is less easy to verify non-trivial floating-point arithmetic operations using such techniques. The natural specifications, including the IEEE Standard, are based on real numbers, not bit-stri... |

141 | Thorough static analysis of device drivers - Ball, Bounimova, et al. - 2006 |

86 | Theorem Proving with the Real Numbers
- Harrison
- 1998
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Citation Context .... 3 Examples We will now give a brief overview of some of our verification projects using HOL Light. Of course, a significant component is the formalization of background theories of pure mathematics =-=[7]-=- and floating-point arithmetic [8]. We will not dwell on that in much detail, but it is an essential prerequisite for the verifications that are described. Division The Intel® Itanium® architecture pe... |

70 |
IA-64 and Elementary Functions: Speed and Precision
- Markstein
- 2000
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Citation Context ...as part of the process of formalization we observed that one of the hypotheses in a key theorem of [14] was stronger than necessary. As a result, we were able to design some more efficient algorithms =-=[13]-=-. Square root Similarly, the Intel® Itanium® architecture defers square roots to software, and we have verified a number of sequences for the operation [11]. The process of formal verification 1 See h... |

69 | HOL Light: A tutorial introduction
- Harrison
- 1996
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Citation Context ...heorem proving programs, 1 and quite a few have been applied to floating-point verification, including at least ACL2, Coq, HOL Light and PVS. We will concentrate later on our own work using HOL Light =-=[6]-=-, but this is not meant to disparage other important work being done at Intel and elsewhere in other systems. 3 Examples We will now give a brief overview of some of our verification projects using HO... |

33 | Lifted-FL: A pragmatic implementation of combined model checking and theorem proving - Aagaard, Jones, et al. - 1999 |

31 | A machine-checked theory of floating point arithmetic
- Harrison
- 1999
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Citation Context ...ief overview of some of our verification projects using HOL Light. Of course, a significant component is the formalization of background theories of pure mathematics [7] and floating-point arithmetic =-=[8]-=-. We will not dwell on that in much detail, but it is an essential prerequisite for the verifications that are described. Division The Intel® Itanium® architecture performs division in software or mic... |

30 | A mechanically checked proof of the correctness of the kernel of the AMD5k86 floating-point division algorithm
- Moore, Lynch, et al.
- 1998
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Citation Context ...rticularly interested in formal verification. Moreover, it is not surprising that a considerable amount of effort has been in the floating-point domain, not just at Intel [17, 10, 9], but also at AMD =-=[15, 19]-=- and IBM [20]. Floating-point algorithms have proven themselves difficult to get right. Yet in marked contrast to some other targets for formal verification, it is not hard to come up with widely acce... |

30 |
Formally verifying ieee compliance of floating-point hardware
- O’Leary, Zhao, et al.
- 1999
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Citation Context ...dable that Intel should be particularly interested in formal verification. Moreover, it is not surprising that a considerable amount of effort has been in the floating-point domain, not just at Intel =-=[17, 10, 9]-=-, but also at AMD [15, 19] and IBM [20]. Floating-point algorithms have proven themselves difficult to get right. Yet in marked contrast to some other targets for formal verification, it is not hard t... |

27 |
Specification and verification of concurrent programs in Cesar
- Queille, Sifakis
- 1981
(Show Context)
Citation Context ...ficient implementation [16] have made possible a variety of techniques ranging from simple Boolean equivalence checking of combinational circuits to more advanced model checking of sequential systems =-=[3, 18, 2, 21]-=-. But it is less easy to verify non-trivial floating-point arithmetic operations using such techniques. The natural specifications, including the IEEE Standard, are based on real numbers, not bit-stri... |

26 |
Computation of elementary functions on the
- Markstein
- 1990
(Show Context)
Citation Context ...the verifications that are described. Division The Intel® Itanium® architecture performs division in software or microcode using sequences of ‘fused multiply-adds’, an approach pioneered by Markstein =-=[14]-=-. There are numerous variants depending on the required performance and accuracy characteristics (e.g. IEEE double-precision division with maximum throughput), and quite a few recommended sequences ar... |

25 | Formal verification of floating point trigonometric functions
- Harrison
(Show Context)
Citation Context ...dable that Intel should be particularly interested in formal verification. Moreover, it is not surprising that a considerable amount of effort has been in the floating-point domain, not just at Intel =-=[17, 10, 9]-=-, but also at AMD [15, 19] and IBM [20]. Floating-point algorithms have proven themselves difficult to get right. Yet in marked contrast to some other targets for formal verification, it is not hard t... |

22 | Per Bjesse, and Niklas Eén. Symbolic reachability analysis based on SAT-Solvers - Abdulla - 2000 |

19 | Proving the IEEE correctness of iterative floating-point square root, divide, and remainder algorithms
- Cornea-Hasegan
- 1998
(Show Context)
Citation Context ... for a list, and http://www.cs.ru.nl/ ∼ freek/comparison/index.html for a comparison of the formalization of an elementary mathematical theorem in several.sfollows a methodology established by Cornea =-=[4]-=-. A general analytical proof covers the majority of cases, but a number of potential exceptions are isolated using numbertheoretic techniques and dealt with using an explicit case analysis. Proofs of ... |

18 | Formal verification of IA-64 division algorithms
- Harrison
- 2000
(Show Context)
Citation Context ...dable that Intel should be particularly interested in formal verification. Moreover, it is not surprising that a considerable amount of effort has been in the floating-point domain, not just at Intel =-=[17, 10, 9]-=-, but also at AMD [15, 19] and IBM [20]. Floating-point algorithms have proven themselves difficult to get right. Yet in marked contrast to some other targets for formal verification, it is not hard t... |

12 | Verifying a logic synthesis tool in Nuprl: A case study in software verification - Aagaard, Leeser - 1994 |

9 | Formal verification of square root algorithms
- Harrison
- 2003
(Show Context)
Citation Context ...le to design some more efficient algorithms [13]. Square root Similarly, the Intel® Itanium® architecture defers square roots to software, and we have verified a number of sequences for the operation =-=[11]-=-. The process of formal verification 1 See http://www.cs.ru.nl/ ∼ freek/digimath/index.html for a list, and http://www.cs.ru.nl/ ∼ freek/comparison/index.html for a comparison of the formalization of ... |

9 |
for binary floating point arithmetic, ANSI/IEEE Std 754
- Standard
- 1985
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Citation Context ...accepted formal specifications of how floating-point operations should behave. In fact, many operations are specified almost completely by the IEEE Standard governing binary floating-point arithmetic =-=[12]-=-. However, in some other respects, floating-point operations present a difficult challenge for formal verification. 2 The role of theorem proving In many other areas of verification, significant succe... |

1 | editors. Formal Methods for Hardware Verification - Bernardo, Cimatti |