## Bridging the gap between formal specification and bit-level floating-point arithmetic

Citations: | 2 - 0 self |

### BibTeX

@MISC{Boldo_bridgingthe,

author = {Sylvie Boldo},

title = {Bridging the gap between formal specification and bit-level floating-point arithmetic},

year = {}

}

### OpenURL

### Abstract

Floating-point arithmetic is defined by the IEEE-754 standard and has often been formalized. We propose a new Coq formalization based on the bit-level representation of the standard and we prove strong links between this new formalization and a previous high-level one. In this process, we have defined functions for any rounding mode described by the standard. Our library can now be applied to certify both software and hardware. Developing results in those two dramatically different directions, like no other formal development so far, guarantees that nothing was forgotten or poorly specified in our formalization. It also lets us compare our work with the existing bit-level formalizations developed with other proof assistants.