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» A Machine-Checked Theory of Floating Point Arithmetic
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TPHOL
1999
IEEE
13 years 9 months ago
A Machine-Checked Theory of Floating Point Arithmetic
Abstract. Intel is applying formal verification to various pieces of mathematical software used in Merced, the first implementation of the new IA-64 architecture. This paper discus...
John Harrison
CAV
2009
Springer
123views Hardware» more  CAV 2009»
13 years 9 months ago
On Using Floating-Point Computations to Help an Exact Linear Arithmetic Decision Procedure
We consider the decision problem for quantifier-free formulas whose atoms are linear inequalities interpreted over the reals or rationals. This problem may be decided using satisf...
David Monniaux
CORR
2010
Springer
118views Education» more  CORR 2010»
13 years 5 months ago
alphaCertified: certifying solutions to polynomial systems
Smale's -theory uses estimates related to the convergence of Newton's method to give criteria implying that Newton iterations will converge quadratically to solutions to ...
Jonathan D. Hauenstein, Frank Sottile
COMPUTING
2006
100views more  COMPUTING 2006»
13 years 5 months ago
Interval Arithmetic with Containment Sets
The idea of containment sets (csets) is due to Walster and Hansen, and the theory is mainly due to the first author. Now that floating point computation with infinities is widely a...
John D. Pryce, George F. Corliss