{"id":397471,"date":"2024-10-20T04:30:26","date_gmt":"2024-10-20T04:30:26","guid":{"rendered":"https:\/\/pdfstandards.shop\/product\/uncategorized\/ieee-1788-2015-2\/"},"modified":"2024-10-26T08:18:22","modified_gmt":"2024-10-26T08:18:22","slug":"ieee-1788-2015-2","status":"publish","type":"product","link":"https:\/\/pdfstandards.shop\/product\/publishers\/ieee\/ieee-1788-2015-2\/","title":{"rendered":"IEEE 1788-2015"},"content":{"rendered":"

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.<\/p>\n

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PDF Pages<\/th>\nPDF Title<\/th>\n<\/tr>\n
1<\/td>\nIEEE Std 1788\u2122-2015 Front cover <\/td>\n<\/tr>\n
3<\/td>\nTitle page <\/td>\n<\/tr>\n
5<\/td>\nImportant Notices and Disclaimers Concerning IEEE Standards Documents <\/td>\n<\/tr>\n
8<\/td>\nParticipants <\/td>\n<\/tr>\n
10<\/td>\nIntroduction <\/td>\n<\/tr>\n
13<\/td>\nContents <\/td>\n<\/tr>\n
17<\/td>\nIMPORTANT NOTICE <\/td>\n<\/tr>\n
18<\/td>\nPart 1. General Requirements
1. Overview
1.1. Scope
1.2. Purpose
1.3. Inclusions
1.4. Exclusions <\/td>\n<\/tr>\n
19<\/td>\n1.5. Word usage
1.6. The meaning of conformance
1.7. Programming environment considerations <\/td>\n<\/tr>\n
20<\/td>\n1.8. Language considerations
2. Normative references <\/td>\n<\/tr>\n
21<\/td>\n3. Notation, abbreviations, and special terms
3.1. Frequently used notation and abbreviations
3.2. Special terms <\/td>\n<\/tr>\n
26<\/td>\n4. Conformance
4.1. Conformance overview <\/td>\n<\/tr>\n
27<\/td>\n4.2. Set-based interval arithmetic
4.2.1. IEEE 754 conformance
4.2.2. Compressed decorated interval arithmetic
4.3. Conformance claim <\/td>\n<\/tr>\n
28<\/td>\n4.4. Implementation conformance questionnaire <\/td>\n<\/tr>\n
29<\/td>\n5. Structure of the standard in levels <\/td>\n<\/tr>\n
30<\/td>\n6. Functions and expressions
6.1. Function definitions <\/td>\n<\/tr>\n
31<\/td>\n6.2. Expression definitions <\/td>\n<\/tr>\n
33<\/td>\n6.3. Function libraries <\/td>\n<\/tr>\n
34<\/td>\n6.4. The FTIA <\/td>\n<\/tr>\n
35<\/td>\n6.5. Related issues
7. Flavors
7.1. Flavors overview <\/td>\n<\/tr>\n
36<\/td>\n7.2. Flavor basic properties <\/td>\n<\/tr>\n
37<\/td>\n7.3. Common evaluations
7.4. Primary versions and Level 1 interval versions
7.4.1. Arithmetic operations <\/td>\n<\/tr>\n
38<\/td>\n7.4.2. Nonarithmetic operations required in all flavors
7.4.3. Flavor-defined nonarithmetic operations
7.5. The relation of Level 1 to Level 2 <\/td>\n<\/tr>\n
39<\/td>\n7.5.1. Types
7.5.2. Hull
7.5.3. Level 2 operations <\/td>\n<\/tr>\n
40<\/td>\n7.5.4. Measures of accuracy <\/td>\n<\/tr>\n
41<\/td>\n8. Decoration system
8.1. Decorations overview <\/td>\n<\/tr>\n
42<\/td>\n8.2. Decoration definition and propagation
8.3. Recognizing common evaluation <\/td>\n<\/tr>\n
43<\/td>\n9. Operations and related items required in all flavors
9.1. Arithmetic operations <\/td>\n<\/tr>\n
45<\/td>\n9.2. 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 <\/td>\n<\/tr>\n
46<\/td>\n9.7. All-flavor interval and number literals
9.7.1. Overview <\/td>\n<\/tr>\n
47<\/td>\n9.7.2. 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 <\/td>\n<\/tr>\n
48<\/td>\n9.7.6. Grammar for all-flavor literals
9.8. Constructors <\/td>\n<\/tr>\n
50<\/td>\nPart 2. Set-Based Intervals
10. Level 1 description
10.1. Non-interval Level 1 entities
10.2. Intervals <\/td>\n<\/tr>\n
51<\/td>\n10.3. Hull
10.4. Functions and expressions <\/td>\n<\/tr>\n
52<\/td>\n10.5. 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 <\/td>\n<\/tr>\n
53<\/td>\n10.5.5. Two-output division <\/td>\n<\/tr>\n
54<\/td>\n10.5.6. Cancellative addition and subtraction
10.5.7. Set operations
10.5.8. Constructors <\/td>\n<\/tr>\n
55<\/td>\n10.5.9. Numeric functions of intervals
10.5.10. Boolean functions of intervals <\/td>\n<\/tr>\n
56<\/td>\n10.6. Recommended operations
10.6.1. Forward-mode elementary functions <\/td>\n<\/tr>\n
57<\/td>\n10.6.2. Slope functions
10.6.3. Boolean functions of intervals
10.6.4. Extended interval comparisons <\/td>\n<\/tr>\n
60<\/td>\n11. The decoration system at Level 1
11.1. Decorations and decorated intervals overview
11.2. Definitions and basic properties <\/td>\n<\/tr>\n
61<\/td>\n11.3. The ill-formed interval
11.4. Permitted combinations
11.5. Operations on\/with decorations
11.5.1. Initializing <\/td>\n<\/tr>\n
62<\/td>\n11.5.2. Disassembling and assembling
11.5.3. Comparisons
11.6. Decorations and arithmetic operations <\/td>\n<\/tr>\n
63<\/td>\n11.7. Decoration of non-arithmetic operations
11.7.1. Interval-valued operations
11.7.2. Non-interval-valued operations
11.8. User-supplied functions <\/td>\n<\/tr>\n
64<\/td>\n11.9. Notes on the com decoration <\/td>\n<\/tr>\n
65<\/td>\n11.10. Compressed arithmetic with a threshold (optional)
11.10.1. Motivation
11.10.2. Compressed interval types <\/td>\n<\/tr>\n
66<\/td>\n11.10.3. Operations <\/td>\n<\/tr>\n
67<\/td>\n12. Level 2 description
12.1. Level 2 introduction
12.1.1. Types and formats
12.1.2. Operations <\/td>\n<\/tr>\n
68<\/td>\n12.1.3. Exception behavior
12.2. Naming conventions for operations
12.3. Tagging, and the meaning of equality at Level 2 <\/td>\n<\/tr>\n
69<\/td>\n12.4. Number formats <\/td>\n<\/tr>\n
70<\/td>\n12.5. Bare and decorated interval types
12.5.1. Definition <\/td>\n<\/tr>\n
71<\/td>\n12.5.2. 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 <\/td>\n<\/tr>\n
72<\/td>\n12.8. 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 <\/td>\n<\/tr>\n
73<\/td>\n12.10. Accuracy of operations
12.10.1. Measures of accuracy <\/td>\n<\/tr>\n
74<\/td>\n12.10.2. Accuracy requirements
12.10.3. Documentation requirements
12.11. Interval and number literals
12.11.1. Overview
12.11.2. Number literals <\/td>\n<\/tr>\n
75<\/td>\n12.11.3. Bare intervals
12.11.4. Decorated intervals
12.11.5. Grammar for portable literals <\/td>\n<\/tr>\n
76<\/td>\n12.12. Required operations on bare and decorated intervals
12.12.1. Interval constants <\/td>\n<\/tr>\n
77<\/td>\n12.12.2. Forward-mode elementary functions
12.12.3. Two-output division
12.12.4. Reverse-mode elementary functions
12.12.5. Cancellative addition and subtraction <\/td>\n<\/tr>\n
78<\/td>\n12.12.6. Set operations
12.12.7. Constructors <\/td>\n<\/tr>\n
79<\/td>\n12.12.8. Numeric functions of intervals <\/td>\n<\/tr>\n
80<\/td>\n12.12.9. Boolean functions of intervals <\/td>\n<\/tr>\n
81<\/td>\n12.12.10. Interval type conversion
12.12.11. Operations on\/with decorations
12.12.12. Reduction operations <\/td>\n<\/tr>\n
82<\/td>\n12.13. 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 <\/td>\n<\/tr>\n
83<\/td>\n13. Input and output (I\/O) of intervals
13.1. Overview
13.2. Input
13.3. Output <\/td>\n<\/tr>\n
84<\/td>\n13.4. Exact text representation <\/td>\n<\/tr>\n
85<\/td>\n13.4.1. Conversion of IEEE 754 numbers to strings <\/td>\n<\/tr>\n
86<\/td>\n13.4.2. Exact representations of comparable types
14. Levels 3 and 4 description
14.1. Overview
14.2. Representation <\/td>\n<\/tr>\n
87<\/td>\n14.3. Operations and representation
14.4. Interchange representations and encodings <\/td>\n<\/tr>\n
90<\/td>\nAnnex A (informative) Bibliography <\/td>\n<\/tr>\n
92<\/td>\nAnnex B (informative) The fundamental theorem of decorated interval arithmetic for the set-based flavor
B1. Preliminaries <\/td>\n<\/tr>\n
94<\/td>\nB2. The theorem <\/td>\n<\/tr>\n
97<\/td>\nBack cover <\/td>\n<\/tr>\n<\/table>\n","protected":false},"excerpt":{"rendered":"

IEEE Standard for Interval Arithmetic<\/b><\/p>\n\n\n\n\n
Published By<\/td>\nPublication Date<\/td>\nNumber of Pages<\/td>\n<\/tr>\n
IEEE<\/b><\/a><\/td>\n2015<\/td>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"featured_media":397473,"template":"","meta":{"rank_math_lock_modified_date":false,"ep_exclude_from_search":false},"product_cat":[2644],"product_tag":[],"class_list":{"0":"post-397471","1":"product","2":"type-product","3":"status-publish","4":"has-post-thumbnail","6":"product_cat-ieee","8":"first","9":"instock","10":"sold-individually","11":"shipping-taxable","12":"purchasable","13":"product-type-simple"},"_links":{"self":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product\/397471","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product"}],"about":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/types\/product"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media\/397473"}],"wp:attachment":[{"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/media?parent=397471"}],"wp:term":[{"taxonomy":"product_cat","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_cat?post=397471"},{"taxonomy":"product_tag","embeddable":true,"href":"https:\/\/pdfstandards.shop\/wp-json\/wp\/v2\/product_tag?post=397471"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}