ISO/IEC/IEEE 60559:2011
(Main)Information technology — Microprocessor Systems — Floating-Point arithmetic
Information technology — Microprocessor Systems — Floating-Point arithmetic
ISO/IEC/IEEE 60559:2011(E) specifies formats and methods for floating-point arithmetic in computer systems - standard and extended functions with single, double, extended, and extendable precision and recommends formats for data interchange. Exception conditions are defined and standard handling of these conditions is specified. It provides a method for computation with floating-point numbers that will yield the same result whether the processing is done in hardware, software, or a combination of the two. The results of the computation will be identical, independent of implementation, given the same input data. Errors, and error conditions, in the mathematical processing will be reported in a consistent manner regardless of implementation. This first edition, published as ISO/IEC/IEEE 60559, replaces the second edition of IEC 60559.
Technologies de l'information — Systèmes de microprocesseurs — Arithmétique flottante
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ISO/IEC/IEEE 60559
Edition 1.0 2011-06
INTERNATIONAL
STANDARD
Information technology – Microprocessor Systems – Floating-Point arithmetic
ISO/IEC/IEEE 60559:2011(E)
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ISO/IEC/IEEE 60559
Edition 1.0 2011-06
INTERNATIONAL
STANDARD
Information technology – Microprocessor Systems – Floating-Point arithmetic
INTERNATIONAL
ELECTROTECHNICAL
COMMISSION
PRICE CODE
U
ICS 35.200 ISBN 978-2-88912-566-1
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ISO/IEC/IEEE FDIS 60559:2010(E)
Contents
1. Overview .1
1.1 Scope .1
1.2 Purpose .1
1.3 Inclusions .1
1.4 Exclusions .2
1.5 Programming environment considerations .2
1.6 Word usage .2
2. Definitions, abbreviations, and acronyms .3
2.1 Definitions .3
2.2 Abbreviations and acronyms .5
3. Floating-point formats .6
3.1 Overview .6
3.2 Specification levels .7
3.3 Sets of floating-point data .7
3.4 Binary interchange format encodings .9
3.5 Decimal interchange format encodings .10
3.6 Interchange format parameters .13
3.7 Extended and extendable precisions .14
4. Attributes and rounding .15
4.1 Attribute specification .15
4.2 Dynamic modes for attributes .15
4.3 Rounding-direction attributes .16
5. Operations .17
5.1 Overview .17
5.2 Decimal exponent calculation .18
5.3 Homogeneous general-computational operations .19
5.4 formatOf general-computational operations .21
5.5 Quiet-computational operations .23
5.6 Signaling-computational operations .24
5.7 Non-computational operations .24
5.8 Details of conversions from floating-point to integer formats .26
5.9 Details of operations to round a floating-point datum to integral value .27
5.10 Details of totalOrder predicate .28
5.11 Details of comparison predicates .29
5.12 Details of conversion between floating-point data and external character sequences .30
6. Infinity, NaNs, and sign bit .34
6.1 Infinity arithmetic .34
6.2 Operations with NaNs .34
6.3 The sign bit .35
7. Default exception handling .36
7.1 Overview: exceptions and flags .36
7.2 Invalid operation .37
7.3 Division by zero .37
7.4 Overflow .37
7.5 Underflow .38
7.6 Inexact .38
8. Alternate exception handling attributes .39
8.1 Overview .39
8.2 Resuming alternate exception handling attributes .39
8.3 Immediate and delayed alternate exception handling attributes .40
Copyright © IEEE 2008. All rights reserved i
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ISO/IEC/IEEE 60559:2011(E)
9. Recommended operations .41
9.1 Conforming language- and implementation-defined functions .41
9.2 Recommended correctly rounded functions .42
9.3 Operations on dynamic modes for attributes .46
9.4 Reduction operations .46
10. Expression evaluation .48
10.1 Expression evaluation rules .48
10.2 Assignments, parameters, and function values .48
10.3 preferredWidth attributes for expression evaluation .49
10.4 Literal meaning and value-changing optimizations .50
11. Reproducible floating-point results .51
Annex A (informative) Bibliography .53
Annex B (informative) Program debugging support .55
Index of operations .57
ii Copyright © IEEE 2008. All rights reserved
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Foreword
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ISO/IEC/IEEE 60559 was prepared by the Microprocessor Standards Committee of the IEEE Computer Society
of the IEEE (as IEEE 754-2008). It was adopted by Joint Technical Committee ISO/IEC JTC 1, Information
technology, Subcommittee SC 25, Interconnection of information technology equipment in parallel with its approval
by the ISO/IEC national bodies, under the “fast-track procedure” defined in the Partner Standards Development
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document with participation and input from ISO/IEC national bodies.
This first edition, published as ISO/IEC/IEEE 60559, replaces the second edition of IEC 60559.
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ISO/IEC/IEEE 60559:2011(E)
IEEE Introduction
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This introduction is not part of IEEE Std 754-2008, IEEE Standard for Floating-Point Arithmetic.
This standard is a product of the Floating-Point Working Group of, and sponsored by, the Microprocessor
Standards Committee of the IEEE Computer Society.
This standard provides a discipline for performing floating-point computation that yields results
independent of whether the processing is done in hardware, software, or a combination of the two. For
operations specified in the normative part of this standard, numerical results and exceptions are uniquely
determined by the values of the input data, the operation, and the destination, all under user control.
This standard defines a family of commercially feasible ways for systems to perform binary and decimal
floating-point arithmetic. Among the desiderata that guided the formulation of this standard were:
a) Facilitate movement of existing programs from diverse computers to those that adhere to this
standard as well as among those that adhere to this standard.
b) Enhance the capabilities and safety available to users and programmers who, although not expert
in numerical methods, might well be attempting to produce numerically sophisticated programs.
c) Encourage experts to develop and distribute robust and efficient numerical programs that are
portable, by way of minor editing and recompilation, onto any computer that conforms to this
standard and possesses adequate capacity. Together with language controls it should be possible to
write programs that produce identical results on all conforming systems.
d) Provide direct support for
― execution-time diagnosis of anomalies
― smoother handling of exceptions
― interval arithmetic at a reasonable cost.
e) Provide for development of
― standard elementary functions such as exp and cos
― high precision (multiword) arithmetic
― coupled numerical and symbolic algebraic computation.
f) Enable rather than preclude further refinements and extensions.
In programming environments, this standard is also intended to form the basis for a dialog between the
numerical community and programming language designers. It is hoped that language-defined methods for
the control of expression evaluation and exceptions might be defined in coming years, so that it will be
possible to write programs that produce identical results on all conforming systems. However, it is
recognized that utility and safety in languages are sometimes antagonists, as are efficiency and portability.
Therefore, it is hoped that language designers will look on the full set of operation, precision, and exception
controls described here as a guide to providing the programmer with the ability to portably control
expressions and exceptions. It is also hoped that designers will be guided by this standard to provide
extensions in a completely portable way.
Copyright © IEEE 2008. All rights reserved v
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ISO/IEC/IEEE 60559:2011(E)
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Patents
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Copyright © IEEE 2008. All rights reserved vii
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ISO/IEC/IEEE 60559:2011(E)
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Floating-Point arithmetic
IMPORTANT NOTICE: This standard is not intended to assure safety, security, health, or environmental
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1.0
1. Overview
1.1.0
1.1 Scope
This standard specifies formats and methods for floating-point arithmetic in computer systems—standard
and extended functions with single, double, extended, and extendable precision—and recommends formats
for data interchange. Exception conditions are defined and standard handling of these conditions is
specified.
1.2.0
1.2 Purpose
This standard provides a method for computation with floating-point numbers that will yield the same result
whether the processing is done in hardware, software, or a combination of the two. The results of the
computation will be identical, independent of implementation, given the same input data. Errors, and error
conditions, in the mathematical processing will be reported in a consistent manner regardless of
implementation.
1.3.0
1.3 Inclusions
This standard specifies:
― Formats for binary and decimal floating-point data, for computation and data interchange.
― Addition, subtraction, multiplication, division, fused multiply add, square root, compare, and other
oper
...
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