IEEE 1788-2015

$59.58

IEEE Standard for Interval Arithmetic

Published By	Publication Date	Number of Pages
IEEE	2015

Guaranteed Safe Checkout

Category: IEEE

If you have any questions, feel free to reach out to our online customer service team by clicking on the bottom right corner. We’re here to assist you 24/7.
Email:[email protected]

Description

New IEEE Standard – Active. This standard specifies basic interval arithmetic (IA) operations selecting and following one of the commonly used mathematical interval models. This standard supports the IEEE 754 floating point formats of practical use in interval computations. Exception conditions are defined, and standard handling of these conditions is specified. Consistency with the interval model is tempered with practical considerations based on input from representatives of vendors, developers and maintainers of existing systems. The standard provides a layer between the hardware and the programming language levels. It does not mandate that any operations be implemented in hardware. It does not define any realization of the basic operations as functions in a programming language.

PDF Catalog

PDF Pages	PDF Title
1	IEEE Std 1788™-2015 Front cover
3	Title page
5	Important Notices and Disclaimers Concerning IEEE Standards Documents
8	Participants
10	Introduction
13	Contents
17	IMPORTANT NOTICE
18	Part 1. General Requirements 1. Overview 1.1. Scope 1.2. Purpose 1.3. Inclusions 1.4. Exclusions
19	1.5. Word usage 1.6. The meaning of conformance 1.7. Programming environment considerations
20	1.8. Language considerations 2. Normative references
21	3. Notation, abbreviations, and special terms 3.1. Frequently used notation and abbreviations 3.2. Special terms
26	4. Conformance 4.1. Conformance overview
27	4.2. Set-based interval arithmetic 4.2.1. IEEE 754 conformance 4.2.2. Compressed decorated interval arithmetic 4.3. Conformance claim
28	4.4. Implementation conformance questionnaire
29	5. Structure of the standard in levels
30	6. Functions and expressions 6.1. Function definitions
31	6.2. Expression definitions
33	6.3. Function libraries
34	6.4. The FTIA
35	6.5. Related issues 7. Flavors 7.1. Flavors overview
36	7.2. Flavor basic properties
37	7.3. Common evaluations 7.4. Primary versions and Level 1 interval versions 7.4.1. Arithmetic operations
38	7.4.2. Nonarithmetic operations required in all flavors 7.4.3. Flavor-defined nonarithmetic operations 7.5. The relation of Level 1 to Level 2
39	7.5.1. Types 7.5.2. Hull 7.5.3. Level 2 operations
40	7.5.4. Measures of accuracy
41	8. Decoration system 8.1. Decorations overview
42	8.2. Decoration definition and propagation 8.3. Recognizing common evaluation
43	9. Operations and related items required in all flavors 9.1. Arithmetic operations
45	9.2. Cancellative addition and subtraction 9.3. Set operations 9.4. Numeric functions of intervals 9.5. Boolean functions of intervals 9.6. Operations on/with decorations
46	9.7. All-flavor interval and number literals 9.7.1. Overview
47	9.7.2. All-flavor number literals 9.7.3. Unit in last place 9.7.4. All-flavor bare interval literals 9.7.5. All-flavor decorated interval literals
48	9.7.6. Grammar for all-flavor literals 9.8. Constructors
50	Part 2. Set-Based Intervals 10. Level 1 description 10.1. Non-interval Level 1 entities 10.2. Intervals
51	10.3. Hull 10.4. Functions and expressions
52	10.5. Required operations 10.5.1. Interval literals 10.5.2. Interval constants 10.5.3. Forward-mode elementary functions 10.5.4. Reverse-mode elementary functions
53	10.5.5. Two-output division
54	10.5.6. Cancellative addition and subtraction 10.5.7. Set operations 10.5.8. Constructors
55	10.5.9. Numeric functions of intervals 10.5.10. Boolean functions of intervals
56	10.6. Recommended operations 10.6.1. Forward-mode elementary functions
57	10.6.2. Slope functions 10.6.3. Boolean functions of intervals 10.6.4. Extended interval comparisons
60	11. The decoration system at Level 1 11.1. Decorations and decorated intervals overview 11.2. Definitions and basic properties
61	11.3. The ill-formed interval 11.4. Permitted combinations 11.5. Operations on/with decorations 11.5.1. Initializing
62	11.5.2. Disassembling and assembling 11.5.3. Comparisons 11.6. Decorations and arithmetic operations
63	11.7. Decoration of non-arithmetic operations 11.7.1. Interval-valued operations 11.7.2. Non-interval-valued operations 11.8. User-supplied functions
64	11.9. Notes on the com decoration
65	11.10. Compressed arithmetic with a threshold (optional) 11.10.1. Motivation 11.10.2. Compressed interval types
66	11.10.3. Operations
67	12. Level 2 description 12.1. Level 2 introduction 12.1.1. Types and formats 12.1.2. Operations
68	12.1.3. Exception behavior 12.2. Naming conventions for operations 12.3. Tagging, and the meaning of equality at Level 2
69	12.4. Number formats
70	12.5. Bare and decorated interval types 12.5.1. Definition
71	12.5.2. Inf-sup and mid-rad types 12.6. 754-conformance 12.6.1. Definition 12.6.2. 754-conforming mixed-type operations 12.7. Multi-precision interval types
72	12.8. Explicit and implicit types, and Level 2 hull operation 12.8.1. Hull in one dimension 12.8.2. Hull in several dimensions 12.9. Level 2 interval extensions
73	12.10. Accuracy of operations 12.10.1. Measures of accuracy
74	12.10.2. Accuracy requirements 12.10.3. Documentation requirements 12.11. Interval and number literals 12.11.1. Overview 12.11.2. Number literals
75	12.11.3. Bare intervals 12.11.4. Decorated intervals 12.11.5. Grammar for portable literals
76	12.12. Required operations on bare and decorated intervals 12.12.1. Interval constants
77	12.12.2. Forward-mode elementary functions 12.12.3. Two-output division 12.12.4. Reverse-mode elementary functions 12.12.5. Cancellative addition and subtraction
78	12.12.6. Set operations 12.12.7. Constructors
79	12.12.8. Numeric functions of intervals
80	12.12.9. Boolean functions of intervals
81	12.12.10. Interval type conversion 12.12.11. Operations on/with decorations 12.12.12. Reduction operations
82	12.13. Recommended operations 12.13.1. Forward-mode elementary functions 12.13.2. Slope functions 12.13.3. Boolean functions of intervals 12.13.4. Extended interval comparisons 12.13.5. Exact reduction operations
83	13. Input and output (I/O) of intervals 13.1. Overview 13.2. Input 13.3. Output
84	13.4. Exact text representation
85	13.4.1. Conversion of IEEE 754 numbers to strings
86	13.4.2. Exact representations of comparable types 14. Levels 3 and 4 description 14.1. Overview 14.2. Representation
87	14.3. Operations and representation 14.4. Interchange representations and encodings
90	Annex A (informative) Bibliography
92	Annex B (informative) The fundamental theorem of decorated interval arithmetic for the set-based flavor B1. Preliminaries
94	B2. The theorem
97	Back cover