abstract={The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and portably. Many hardware floating-point units use the IEEE 754 standard. The standard defines: arithmetic formats: sets of binary and decimal floating-point data, which consist of finite numbers (including signed zeros and subnormal numbers), infinities, and special "not a number" values (NaNs) interchange formats: encodings (bit strings) that may be used to exchange floating-point data in an efficient and compact form rounding rules: properties to be satisfied when rounding numbers during arithmetic and conversions operations: arithmetic and other operations (such as trigonometric functions) on arithmetic formats exception handling: indications of exceptional conditions (such as division by zero, overflow, etc.)IEEE 754-2008, published in August 2008, includes nearly all of the original IEEE 754-1985 standard, plus the IEEE 854-1987 Standard for Radix-Independent Floating-Point Arithmetic. The current version, IEEE 754-2019, was published in July 2019. It is a minor revision of the previous version, incorporating mainly clarifications, defect fixes and new recommended operations.},
title={{{IEEE}} 754-2019 - {{IEEE Standard}} for {{Floating}}-{{Point Arithmetic}}},
year={2019},
pages={1--84},
doi={10.1109/IEEESTD.2019.8766229},
abstract={This standard specifies interchange and arithmetic formats and methods for binary and decimal floating-point arithmetic in computer programming environments. This standard specifies exception conditions and their default handling. An implementation of a floating-point system conforming to this standard may be realized entirely in software, entirely in hardware, or in any combination of software and hardware. For operations specified in the normative part of this standard, numerical results and exceptions are uniquely determined by the values of the input data, sequence of operations, and destination formats, all under user control.},
title={Certifying Floating-Point Implementations Using {{Gappa}}},
@article{dedinechin2011certifyingfloatingpoint,
title={Certifying the Floating-Point Implementation of an Elementary Function Using {{Gappa}}},
author={{de Dinechin}, Florent and Lauter, Christoph and Melquiond, Guillaume},
pages={21},
abstract={High confidence in floating-point programs requires proving numerical properties of final and intermediate values. One may need to guarantee that a value stays within some range, or that the error relative to some ideal value is well bounded. Such work may require several lines of proof for each line of code, and will usually be broken by the smallest change to the code (e.g. for maintenance or optimization purpose). Certifying these programs by hand is therefore very tedious and error-prone. This article discusses the use of the Gappa proof assistant in this context. Gappa has two main advantages over previous approaches: Its input format is very close to the actual C code to validate, and it automates error evaluation and propagation using interval arithmetic. Besides, it can be used to incrementally prove complex mathematical properties pertaining to the C code. Yet it does not require any specific knowledge about automatic theorem proving, and thus is accessible to a wide community. Moreover, Gappa may generate a formal proof of the results that can be checked independently by a lower-level proof assistant like Coq, hence providing an even higher confidence in the certification of the numerical code. The article demonstrates the use of this tool on a real-size example, an elementary function with correctly rounded output.},
file={/home/antonin/Zotero/storage/NBYNQ7A5/de Dinechin et al. - Certifying floating-point implementations using Gap.pdf},
