IEEE 1788.1-2017

$37.92

IEEE Standard for Interval Arithmetic (Simplified)

Published By	Publication Date	Number of Pages
IEEE	2017

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Description

New IEEE Standard – Active. This standard is a simplified version and a subset of the IEEE Std 1788TM-2015 for Interval Arithmetic and includes those operations and features of the latter that in the the editors’ view are most commonly used in practice. IEEE Std 1788.1-2017 specifies interval arithmetic operations based on intervals whose endpoints are IEEE Std 754TM-2008 binary64 floating-point numbers and a decoration system for exception-free computations and propagation of properties of the computed results. A program built on top of an implementation of IEEE Std 1788.1-2017 should compile and run, and give identical output within round off, using an implementation of IEEE Std 1788-2015, or any superset of the former. Compared to IEEE Std 1788-2015, this standard aims to be minimalistic, yet to cover much of the functionality needed for interval computations. As such, it is more accessible and will be much easier to implement, and thus will speed up production of implementations.

PDF Catalog

PDF Pages	PDF Title
1	IEEE Std 1788.1™-2017 (Front Cover)
2	Title page
4	Important Notices and Disclaimers Concerning IEEE Standards Documents
7	Participants
9	Introduction
10	Contents
11	Part 1. General Requirements 1. Overview 1.1. Scope 1.2. Purpose 1.3. Word usage
12	1.4. Structure of the standard in levels 1.5. The meaning of conformance 2. Normative references 3. Special terms, abbreviations, and notation 3.1. Frequently used notation and abbreviations 3.2. Special terms accuracy mode
13	arithmetic operation bare interval bounds box constant datum decoration decorated interval domain elementary function exception
14	expression fma FTIA, FTDIA function hull implementation inf-sup interval interval extension interval vector library map, mapping mathematical interval of constructor NaI, NaN
15	no value non-arithmetic operation number octet point function range string, text tightest tightness type
16	Part 2. Interval Standard (Simplified) 4. Level 1 description 4.1. Level 1 entities 4.2. Intervals
17	4.3. Hull 4.4. Functions 4.4.1. Function terminology 4.4.2. Point function 4.4.3. Point arithmetic operation
18	4.4.4. Interval-valued functions 4.4.5. Constants 4.5. Required operations 4.5.1. Interval constants 4.5.2. Arithmetic operations
20	4.5.3. Cancellative addition and subtraction 4.5.4. Set operations 4.5.5. Constructors
21	4.5.6. Numeric functions of intervals 4.5.7. Boolean functions of intervals
23	5. The decoration system at Level 1 5.1. Overview 5.2. Definitions and properties
24	5.3. The ill-formed interval 5.4. Permitted combinations 5.5. Operations on/with decorations 5.5.1. Initializing
25	5.5.2. Disassembling and assembling 5.5.3. Comparisons 5.6. Decorations and arithmetic operations 5.7. Decoration of non-arithmetic operations 5.7.1. Interval-valued operations
26	5.7.2. Non-interval-valued operations
27	6. Level 2 description 6.1. Introduction 6.1.1. Interval type 6.1.2. Decorated interval type 6.1.3. Operations 6.1.4. Exception behavior 6.2. Naming conventions for operations
28	6.3. Level 2 hull operation 6.3.1. Hull in one dimension 6.3.2. Hull in n dimensions 6.4. Level 2 interval extensions 6.5. Accuracy of operations 6.5.1. Measures of accuracy
29	6.5.2. Accuracy requirements 6.5.3. Documentation requirements 6.6. Number and interval literals 6.6.1. Number literals
30	6.6.2. Bare intervals 6.6.3. Decorated intervals 6.7. Required operations 6.7.1. Interval constants 6.7.2. Elementary functions
31	6.7.3. Cancellative addition and subtraction 6.7.4. Set operations 6.7.5. Constructors
32	6.7.6. Numeric functions of intervals
33	6.7.7. Boolean functions of intervals 6.7.8. Operations on/with decorations
34	6.8. Input and output (I/O) of intervals 6.8.1. Overview 6.8.2. Input 6.8.3. Output
35	7. Levels 3 and 4 description 7.1. Representation 7.2. Operations and representation 7.3. Interchange representations and encodings
37	Annex A. Features of the full standard IEEE Std 1788-2015 not required in the IEEE Std 1788.1-2017 standard (informative)