ISO IEC IEEE 60559-2011 Information technology - Microprocessor Systems - Floating-Point arithmetic《信息技术 微处理器系统 浮点算法》.pdf

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1、 ISO/IEC/IEEE 60559 Edition 1.0 2011-06 INTERNATIONAL STANDARD Information technology Microprocessor Systems Floating-Point arithmetic ISO/IEC/IEEE 60559:2011(E) THIS PUBLICATION IS COPYRIGHT PROTECTED Copyright 2011 IEEE All rights reserved. Unless otherwise specified, no part of this publication m

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9、 COMMISSION U ICS 35.200 PRICE CODE ISBN 978-2-88912-566-1 Information technology Microprocessor Systems Floating-Point arithmetic 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, abbr

10、eviations, 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 parame

11、ters .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 ope

12、rations .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-poin

13、t 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 Th

14、e 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 attribut

15、es 39 8.3 Immediate and delayed alternate exception handling attributes .40Copyright IEEE 2008. All rights reserved i ISO/IEC/IEEE FDIS 60559:2010(E) 9. Recommended operations 41 9.1 Conforming language- and implementation-defined functions 41 9.2 Recommended correctly rounded functions .42 9.3 Oper

16、ations 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 optimizatio

17、ns 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 ISO/IEC/IEEE 60559:2011(E) Foreword ISO (the International Organization for Standardization)

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46、rtions of any individual standard for educational classroom use can also be obtained through the Copyright Clearance Center. IEEE IntroductionISO/IEC/IEEE 60559:2011(E)This introduction is not part of IEEE Std 754-2008, IEEE Standard for Floating-Point Arithmetic. This standard is a product of the F

47、loating-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 combinati

48、on 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 syste

49、ms 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