IEEE 754 2019

$53.08

IEEE Standard for Floating-Point Arithmetic

Published By	Publication Date	Number of Pages
IEEE	2019	84

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Description

Revision Standard – Active. 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.

PDF Catalog

PDF Pages	PDF Title
1	IEEE Std 754™-2019 Front Cover
2	Title page
4	Important Notices
7	Participants
9	Introduction
10	Contents
12	1. Overview 1.1 Scope 1.2 Purpose 1.3 Inclusions 1.4 Exclusions
13	1.5 Programming environment considerations 1.6 Word usage
14	2. Definitions, abbreviations, and acronyms 2.1 Definitions
16	2.2 Abbreviations and acronyms
17	3. Floating-point formats 3.1 Overview 3.1.1 Formats 3.1.2 Conformance
18	3.2 Specification levels 3.3 Sets of floating-point data
20	3.4 Binary interchange format encodings
21	3.5 Decimal interchange format encodings 3.5.1 Cohorts 3.5.2 Encodings
24	3.6 Interchange format parameters
26	3.7 Extended and extendable precisions
27	4. Attributes and rounding 4.1 Attribute specification 4.2 Dynamic modes for attributes
28	4.3 Rounding-direction attributes 4.3.1 Rounding-direction attributes to nearest 4.3.2 Directed rounding attributes
29	4.3.3 Rounding attribute requirements
30	5. Operations 5.1 Overview
31	5.2 Decimal exponent calculation
32	5.3 Homogeneous general-computational operations 5.3.1 General operations
33	5.3.2 Decimal operations 5.3.3 logBFormat operations
34	5.4 formatOf general-computational operations 5.4.1 Arithmetic operations
35	5.4.2 Conversion operations for floating-point formats and decimal character sequences 5.4.3 Conversion operations for binary formats
36	5.5 Quiet-computational operations 5.5.1 Sign bit operations
37	5.5.2 Decimal re-encoding operations
38	5.6 Signaling-computational operations 5.6.1 Comparisons 5.7 Non-computational operations 5.7.1 Conformance predicates
39	5.7.2 General operations
40	5.7.3 Decimal operation 5.7.4 Operations on subsets of flags 5.8 Details of conversions from floating-point to integer formats
42	5.9 Details of operations to round a floating-point datum to integral value
43	5.10 Details of totalOrder predicate
44	5.11 Details of comparison predicates
45	5.12 Details of conversion between floating-point data and external character sequences
46	5.12.1 External character sequences representing zeros, infinities, and NaNs 5.12.2 External decimal character sequences representing finite numbers
48	5.12.3 External hexadecimal-significand character sequences representing finite numbers
49	6. Infinity, NaNs, and sign bit 6.1 Infinity arithmetic 6.2 Operations with NaNs 6.2.1 NaN encodings in binary interchange formats
50	6.2.2 NaN encodings in decimal interchange formats 6.2.3 NaN propagation
51	6.3 The sign bit
52	7. Exceptions and default exception handling 7.1 Overview: exceptions and flags
53	7.2 Invalid operation
54	7.3 Division by zero 7.4 Overflow 7.5 Underflow
55	7.6 Inexact
56	8. Alternate exception handling attributes 8.1 Overview 8.2 Resuming alternate exception handling attributes
57	8.3 Immediate and delayed alternate exception handling attributes
59	9. Recommended operations 9.1 Conforming language- and implementation-defined operations 9.2 Additional mathematical operations
62	9.2.1 Special values
65	9.2.2 Preferred exponents
66	9.3 Dynamic mode operations 9.3.1 Operations on individual dynamic modes 9.3.2 Operations on all dynamic modes
67	9.4 Reduction operations
69	9.5 Augmented arithmetic operations
70	9.6 Minimum and maximum operations
72	9.7 NaN payload operations
73	10. Expression evaluation 10.1 Expression evaluation rules 10.2 Assignments, parameters, and function values
74	10.3 preferredWidth attributes for expression evaluation
75	10.4 Literal meaning and value-changing optimizations
76	11. Reproducible floating-point results
78	Annex A (informative) Bibliography
80	Annex B (informative) Program debugging support
82	Annex C (informative) List of operations
84	Back Cover