实例介绍
【实例简介】
ieee-754 2019最新标准。奉献给大家！754-2019 - IEEE Standard for Floating-Point Arithmetic， ieee 浮点标准，2019年
IEEE Std 754-2019 IEEE Standard for Floating-Point arithmeti Abstract: 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 contro Keywords: arithmetic, binary, computer, decimal, exponent, floating-point, format, IEEE 754 TM interchange, Nan, number, rounding, significand, subnormal The Institute of Electrical and Electronics Engineers, Inc 3 Park Avenue. New york. NY 10016-5997 USA Copyright o 2019 by the Institute of Electrical and Electronics Engineers, Inc All rights reserved. Published 22 July 2019. Printed in the United States of America IEEE is a registered trademark in the U.s. Patent Trademark Office, owned by the Institute of Electrical and Electronics Engineers, Incorporated PDF: ISBN 978-1 5924-2 STD23738 Print:|sEN978-15044-59259 STDPD23738 IEEE prohibits discrimination, harassment, and bullying Formoreinformationsvisithttp:/www.leee.org/eb/aboutus/whatis/policies/p9-26.htm/ No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. 2 Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Important Notices and Disclaimers Concerning IEEE Standards Documents ieee documents are made available for use subject to important notices and legal disclaimers. These notices and disclaimers, or a reference to this page, appear in all standards and may be found under the heading"Important Notices and Disclaimers Concerning IEFF Standards Documents. They can also be obtainedonrequestfromIeeEorviewedathttp://standards.ieeeorg/ipr/disclaimers.html Notice and Disclaimer of Liability Concerning the Use of IEEE Standards Documents IEEE Standards documents(standards, recommended practices, and guides), both full-use and trial-use, are developed within IEEE Societies and the Standards Coordinating Committees of the IEEE Standards Association ("IEEE-SA)Standards Board. IEEE (the Institute )develops its standards through a consensus development process, approved by the American National Standards Institute(ANSP), which brings together volunteers representing varied viewpoints and interests to achieve the final product IEEE Standards are documents developed through scientific, academic, and industry-based technical working groups. Volunteers in IEEE working groups are not necessarily members of the Institute and participate without compensation from Ieee. While ieee administers the process and establishes rules to promote fairness in the consensus development process, ieeE does not independently evaluate, test, or verily the accuracy of any of the information or the soundness of any judgments contained in its standards IEEE Standards do not guarantee or ensure safety, security, health, or environmental protection, or ensure against interference with or from other devices or networks. Implementers and users of IEEE Standards documents are responsible for determining and complying with all appropriate safety, security, environmental, health, and interference protection practices and all applicable laws and regulations ieee does not warrant or represent the accuracy or content of the material contained in its standards, and expressly disclaims all warranties(express, implied and statutory) not included in this or any other document relating to the standard, including, but not limited to, the warranties of: merchantability; fitness for a particular purpose: non-infringement; and quality, accuracy, effectiveness, currency, or completeness of material. In addition, ieee disclaims any and all conditions relating to: results; and workmanlike effort IEEE standards documents are supplied“AsIS”and“ WITH ALL FAULTS.” Use of an ieee standard is wholly voluntary. The existence of an IEeE standard does not imply that there are no other ways to produce test, measure, purchase, market or provide other goods and services related to the scope of the iEee standard. Furthermore, the viewpoint expressed at the time a standard is approved and issued is subject to change brought about through developments in the state of the art and comments received from users of the standard In publishing and making its standards available, IEEE is not suggesting or rendering professional or other services for, or on behalf of, any person or entity nor is IEEe undertaking to perform any duty owed by any other person or entity to another. any person utilizing any ieee Standards document, should rely upon his or her own independent judgment in the exercise of reasonable care in any given circumstances or, as appropriate, seek the advice of a competent professional in determining the appropriateness of a given IEEE Standard IN NO EVENT SHALL IEEE BE LIABLE FOR ANY DIRECT INDIRECT INCIDENTAL. SPECIAL. EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES: LOSS OF USE DATA, OR PROFITS OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE PUBLICATION, USE OF, OR RELIANCE UPON ANY STANDARD, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE AND REGARDLESS OF WHETHER SUCH DAMAGE WAS FORESEEABLE Copyright 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Translations The ieee consensus development process involves the review of documents in English only. In the event that an IEEE standard is translated, only the English version published by ieee should be considered the approved IEEE standard Official statements A statement, written or oral, that is not processed in accordance with the IEEE-Sa Standards board Operations Manual shall not be considered or inferred to be the official position of ieee or any of its committees and shall not be considered to be or be relied upon as, a formal position of IFfE. At lectures symposia, seminars, or educational courses, an individual presenting information on IEEE standards shall make it clear that his or her views should be considered the personal views of that individual rather than the formal position of IEEE Comments on standards Comments for revision of IEEE Standards documents are welcome from any interested party, regardless of membership affiliation with IEEE. However, ieee does not provide consulting information or advice pertaining to IEEE Standards documents. Suggestions for changes in documents should be in the form of a proposed change of text, together with appropriate supporting comments. Since IEeE standards represent a consensus of concerned interests. it is important that any responses to comments and questions also receive the concurrence of a balance of interests for this reason ieee and the members of its societies and Standards Coordinating Committees are not able to provide an instant response to comments or questions except in those cases where the matter has previously been addressed. For the same reason, ieee does not respond to interpretation requests. Any person who would like to participate in revisions to an IEEE standard is welcome to join the relevant IEEe working group Comments on standards should be submitted to the following address Secretary. IEEE-sa Standards board 445 Hoes lane Piscataway, NJ08854 USA Laws and regulations Users of iEEE Standards documents should consult all applicable laws and regulations. Compliance with the provisions of any IEEE Standards document does not imply compliance to any applicable regulatory requirements. Implementers of the standard are responsible for observing or referring to the applicable regulatory requirements. Iee does not, by the publication of its standards, intend to urge action that is not in compliance with applicable laws, and these documents may not be construed as doing so Copyrights ieee draft and approved standards are copyrighted by ieee under U.s. and international copyright laws They are made available by IEEE and are adopted for a wide variety of both public and private uses These include both use, by reference, in laws and regulations, and use in private self-regulation, standardization, and the promotion of engineering practices and methods. By making these documents available for use and adoption by public authorities and private users, ieee does not waive any rights in copyright to the documents Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Photocopies Subject to payment of the appropriate fee, IeeE will grant users a limited, non-exclusive license to photocopy portions of any individual standard for company or organizational internal use or individual, non-commercial use only. To arrange for payment of licensing fees, please contact Copyright Clearance Center. Customer Service. 222 Rosewood Drive. Danvers. MA 01923 USA:+1 9787508400. Permission to photocopy portions of any individual standard for educational classroom use can also be obtained through the Copyright Clearance Center. Updating of IEEE Standards documents Users of IEEE Standards documents should be aware that these documents may be superseded at any time by the issuance of new editions or may be amended from time to time through the issuance of amendments, corrigenda, or errata. A current IEEE document at any point in time consists of the current edition of the document together with any amendments corrigenda, or errata then in effect Every IEEE standard is subjected to review at least every ten years. When a document is more than ten years old and has not undergone a revision process, it is reasonable to conclude that its contents, although still of some value, do not wholly reflect the present state of the art. Users are cautioned to check to determine that they have the latest edition of any IEEE standard In order to determine whether a given document is the current edition and whether it has been amended throughtheissuanceofamendmentscorrigendaorerratavisitIeeEXploreathttp:/ieeexplore.ieee.org/ or contact IEEE at the address listed previously. For more information about the IEEE-SA or IEEE's standardsdevelopmentprocessvisittheieee-saWebsiteathttp://standards.ieee.org Errata Errata, if any, for all IEEe standards can be accessed on the Ieee-sa Website at the following URL: http://standards.ieee.org/findstds/errata/index.html.UsersareencouragedtocheckthisUrlforerrata periodically. Patents Attention is called to the possibility that implementation of this standard may require use of subject matter covered by patent rights. By publication of this standard, no position is taken by the ieee with respect to the existence or validity of any patent rights in connection therewith. If a patent holder or patent applicant has filed a statement of assurance via an Accepted Letter of Assurance then the statement is listed on the IeeE-saWebsiteathttp://standards.ieeeorg/about/sasb/patcom/patents.htmlLettersofAssurancemay indicate whether the Submitter is willing or unwilling to grant licenses under patent rights without compensation or under reasonable rates, with reasonable terms and conditions that are demonstrably free of any unfair discrimination to applicants desiring to obtain such licenses Essential Patent Claims may exist for which a Letter of Assurance has not been received The IEee is not responsible for identifying Essential Patent Claims for which a license may be required, for conducting inquiries into the legal validity or scope of Patents Claims, or determining whether any licensing terms or conditions provided in connection with submission of a Letter of Assurance, if any, or in any licensing agreements are reasonable or non-discriminatory. Users of this standard are expressly advised that determination of the validity of any patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Further information may be obtained from the IEEE Standards Association Copyright 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Participants The following participants in the Floating-Point Working Group contributed to the development of this standard David G. Hough, Chair Mike Cowlishaw editor Jonathan bradbury Ivan godard David matula Neil Burgess Roger A. dolliver lan mclntosh David h. c. chen Mrudula gore Richard A. painter Marius cornea Trenton grale Bogdan pasca John h. crawford Michel lack Nathalie revol loe darcy John hauser Jason ricd James demmel Peter C.B. Henderson Eric m. schwarz Florent de dinechin William Kahan James w. thomas Ken docker R. Baker Kearfott Leonard tsai Hossam a.h. fahmy Christoph lauter Fred J. Tydeman Warren E. Ferguson Vincent lefevre Liang-Kai Wang David m. gav David lutz Lee winter Tcrjc Mathison The following individual members of the balloting committee voted on this standard. Balloters might have voted for approval, disapproval, or abstention Robert aiello Randall groves Nick S. A. Nikjoo Amelia Andersdotter Michel lack Richard A painter Israel barrientos Peter harrod John pi Demetrio Bucaneg Jr Chris n. hinds Nathalie revol David h. c. chen Werner hoelzl Jason ried James Cloos David G. Hough Randy saunders Marius cornea Piotr Karocki Eric m. schwarz Mike cowlishaw R. Baker Kearfott James stine James demmel Jim Kulchisky Walter Struppler Ken Docker Christoph lauter James w. thomas Hossam a.h. fahmy Ⅴ incent Lefevre Michael Thompson Andrew fieldsend Edward mccall Leonard tsai David m. gay Jean-Michel Muller Forrest wright H. Glickenste Bruce muschlitz Jian yu Roger A Colliver Ned nedialkov Oren Yuen Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti When the IEEE-SA Standards Board approved this standard on 13 June 2019, it had the following membership Gary Hoffman, Chair Ted Burse Vice Chair Jean-Philippe Faure, Past chair Konstantinos Karachalios, Secretary Masayuki Ariyoshi David. law Annette reilly Stephen D Dukes Joseph levy Dorothy stanley J. Travis griffith Howard li ha w Guido hertz Xiaohui liu Phil Wennblom Christel hunter Kevin lu Philip winston Joseph l. Koepfinger Daleep mohla Howard Wolfman Thomas Koshy Andrew myles Feng w John D. kulick Jingyi Zhou Member emeritus Copyright 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Introduction This introduction is not part of iEEE Std 754-2019, 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 perations specified in the normative part of this standard, numerical results and exceptions are uniquel 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 loating-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 common elementary functions such as exp or 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. Informative annexes provide additional information- Annex a lists bibliographical resources, Annex B suggests programming environment features for debugging support, and Annex C lists all references to the operations of the standard Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Contents 1. Overview 1.1 Scope......,.,…1l 1.2 Purpose 1. 3 Inclusions 1. 4 Exclusions 1.5 Programming environment considerations 12 1.6 Word usage… 2. Definitions, abbreviations, and acronyms ∴13 2.1 Definitions.…… 2.2 Abbreviations and acronyms 15 3. Floating-point fo 3.1 Overview 3.2 Specification levels 17 3.3 Sets of floating-point data 17 3. 4 Binary interchange format encodings. 19 3. 5 Decimal interchange format encodings 20 3.6 Interchange format parameters 3.7 Extended and extendable precisions 4. Attributes and rounding 26 4.1 Attribute specification 4.2 Dynamic modes for attributes.…… 26 4.3 Rounding-direction attributes 5. Operations 5.1 Overview 29 5.2 Decimal exponent calculation 30 5.3 Homogeneous general-computational operations 5.4 formatOf general-computational operations 5.5 Quiet-computational operations 5.6 Signaling-computational operations 37 5.7 Non-computational operations 37 5.8 Details of conversions from floating-point to integer formats 39 5.9 Details of operations to round a floating-point datum to integral value 41 5.10 Details of totalOrder predicate .42 5.11 Details of comparison predicates 43 5.12 Details of conversion between floating-point data and external character sequences 44 6. Infinity, NaNs, and sign bit 6. 1 Infinity arithmetic 48 6.2 Operations with NaNs 6.3Th bit 7. Exceptions and default exception handling 7. 1 Overview: exceptions and flags 7.2 Invalid operation...... 52 7.3 Division by zero 740 verflow............. 7.5 Underflow 555 7.6 Inexact 8. Alternate exception handling attributes. 8. 1 Overview 8.2 Resuming alternate exception handling attributes 8.3 Immediate and delayed alternate exception handling attributes 56 9 Copyright 2019 IEEE. All rights reserved 【实例截图】
【核心代码】
ieee-754 2019最新标准。奉献给大家！754-2019 - IEEE Standard for Floating-Point Arithmetic， ieee 浮点标准，2019年
IEEE Std 754-2019 IEEE Standard for Floating-Point arithmeti Abstract: 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 contro Keywords: arithmetic, binary, computer, decimal, exponent, floating-point, format, IEEE 754 TM interchange, Nan, number, rounding, significand, subnormal The Institute of Electrical and Electronics Engineers, Inc 3 Park Avenue. New york. NY 10016-5997 USA Copyright o 2019 by the Institute of Electrical and Electronics Engineers, Inc All rights reserved. Published 22 July 2019. Printed in the United States of America IEEE is a registered trademark in the U.s. Patent Trademark Office, owned by the Institute of Electrical and Electronics Engineers, Incorporated PDF: ISBN 978-1 5924-2 STD23738 Print:|sEN978-15044-59259 STDPD23738 IEEE prohibits discrimination, harassment, and bullying Formoreinformationsvisithttp:/www.leee.org/eb/aboutus/whatis/policies/p9-26.htm/ No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. 2 Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Important Notices and Disclaimers Concerning IEEE Standards Documents ieee documents are made available for use subject to important notices and legal disclaimers. These notices and disclaimers, or a reference to this page, appear in all standards and may be found under the heading"Important Notices and Disclaimers Concerning IEFF Standards Documents. They can also be obtainedonrequestfromIeeEorviewedathttp://standards.ieeeorg/ipr/disclaimers.html Notice and Disclaimer of Liability Concerning the Use of IEEE Standards Documents IEEE Standards documents(standards, recommended practices, and guides), both full-use and trial-use, are developed within IEEE Societies and the Standards Coordinating Committees of the IEEE Standards Association ("IEEE-SA)Standards Board. IEEE (the Institute )develops its standards through a consensus development process, approved by the American National Standards Institute(ANSP), which brings together volunteers representing varied viewpoints and interests to achieve the final product IEEE Standards are documents developed through scientific, academic, and industry-based technical working groups. Volunteers in IEEE working groups are not necessarily members of the Institute and participate without compensation from Ieee. While ieee administers the process and establishes rules to promote fairness in the consensus development process, ieeE does not independently evaluate, test, or verily the accuracy of any of the information or the soundness of any judgments contained in its standards IEEE Standards do not guarantee or ensure safety, security, health, or environmental protection, or ensure against interference with or from other devices or networks. Implementers and users of IEEE Standards documents are responsible for determining and complying with all appropriate safety, security, environmental, health, and interference protection practices and all applicable laws and regulations ieee does not warrant or represent the accuracy or content of the material contained in its standards, and expressly disclaims all warranties(express, implied and statutory) not included in this or any other document relating to the standard, including, but not limited to, the warranties of: merchantability; fitness for a particular purpose: non-infringement; and quality, accuracy, effectiveness, currency, or completeness of material. In addition, ieee disclaims any and all conditions relating to: results; and workmanlike effort IEEE standards documents are supplied“AsIS”and“ WITH ALL FAULTS.” Use of an ieee standard is wholly voluntary. The existence of an IEeE standard does not imply that there are no other ways to produce test, measure, purchase, market or provide other goods and services related to the scope of the iEee standard. Furthermore, the viewpoint expressed at the time a standard is approved and issued is subject to change brought about through developments in the state of the art and comments received from users of the standard In publishing and making its standards available, IEEE is not suggesting or rendering professional or other services for, or on behalf of, any person or entity nor is IEEe undertaking to perform any duty owed by any other person or entity to another. any person utilizing any ieee Standards document, should rely upon his or her own independent judgment in the exercise of reasonable care in any given circumstances or, as appropriate, seek the advice of a competent professional in determining the appropriateness of a given IEEE Standard IN NO EVENT SHALL IEEE BE LIABLE FOR ANY DIRECT INDIRECT INCIDENTAL. SPECIAL. EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES: LOSS OF USE DATA, OR PROFITS OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE PUBLICATION, USE OF, OR RELIANCE UPON ANY STANDARD, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE AND REGARDLESS OF WHETHER SUCH DAMAGE WAS FORESEEABLE Copyright 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Translations The ieee consensus development process involves the review of documents in English only. In the event that an IEEE standard is translated, only the English version published by ieee should be considered the approved IEEE standard Official statements A statement, written or oral, that is not processed in accordance with the IEEE-Sa Standards board Operations Manual shall not be considered or inferred to be the official position of ieee or any of its committees and shall not be considered to be or be relied upon as, a formal position of IFfE. At lectures symposia, seminars, or educational courses, an individual presenting information on IEEE standards shall make it clear that his or her views should be considered the personal views of that individual rather than the formal position of IEEE Comments on standards Comments for revision of IEEE Standards documents are welcome from any interested party, regardless of membership affiliation with IEEE. However, ieee does not provide consulting information or advice pertaining to IEEE Standards documents. Suggestions for changes in documents should be in the form of a proposed change of text, together with appropriate supporting comments. Since IEeE standards represent a consensus of concerned interests. it is important that any responses to comments and questions also receive the concurrence of a balance of interests for this reason ieee and the members of its societies and Standards Coordinating Committees are not able to provide an instant response to comments or questions except in those cases where the matter has previously been addressed. For the same reason, ieee does not respond to interpretation requests. Any person who would like to participate in revisions to an IEEE standard is welcome to join the relevant IEEe working group Comments on standards should be submitted to the following address Secretary. IEEE-sa Standards board 445 Hoes lane Piscataway, NJ08854 USA Laws and regulations Users of iEEE Standards documents should consult all applicable laws and regulations. Compliance with the provisions of any IEEE Standards document does not imply compliance to any applicable regulatory requirements. Implementers of the standard are responsible for observing or referring to the applicable regulatory requirements. Iee does not, by the publication of its standards, intend to urge action that is not in compliance with applicable laws, and these documents may not be construed as doing so Copyrights ieee draft and approved standards are copyrighted by ieee under U.s. and international copyright laws They are made available by IEEE and are adopted for a wide variety of both public and private uses These include both use, by reference, in laws and regulations, and use in private self-regulation, standardization, and the promotion of engineering practices and methods. By making these documents available for use and adoption by public authorities and private users, ieee does not waive any rights in copyright to the documents Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Photocopies Subject to payment of the appropriate fee, IeeE will grant users a limited, non-exclusive license to photocopy portions of any individual standard for company or organizational internal use or individual, non-commercial use only. To arrange for payment of licensing fees, please contact Copyright Clearance Center. Customer Service. 222 Rosewood Drive. Danvers. MA 01923 USA:+1 9787508400. Permission to photocopy portions of any individual standard for educational classroom use can also be obtained through the Copyright Clearance Center. Updating of IEEE Standards documents Users of IEEE Standards documents should be aware that these documents may be superseded at any time by the issuance of new editions or may be amended from time to time through the issuance of amendments, corrigenda, or errata. A current IEEE document at any point in time consists of the current edition of the document together with any amendments corrigenda, or errata then in effect Every IEEE standard is subjected to review at least every ten years. When a document is more than ten years old and has not undergone a revision process, it is reasonable to conclude that its contents, although still of some value, do not wholly reflect the present state of the art. Users are cautioned to check to determine that they have the latest edition of any IEEE standard In order to determine whether a given document is the current edition and whether it has been amended throughtheissuanceofamendmentscorrigendaorerratavisitIeeEXploreathttp:/ieeexplore.ieee.org/ or contact IEEE at the address listed previously. For more information about the IEEE-SA or IEEE's standardsdevelopmentprocessvisittheieee-saWebsiteathttp://standards.ieee.org Errata Errata, if any, for all IEEe standards can be accessed on the Ieee-sa Website at the following URL: http://standards.ieee.org/findstds/errata/index.html.UsersareencouragedtocheckthisUrlforerrata periodically. Patents Attention is called to the possibility that implementation of this standard may require use of subject matter covered by patent rights. By publication of this standard, no position is taken by the ieee with respect to the existence or validity of any patent rights in connection therewith. If a patent holder or patent applicant has filed a statement of assurance via an Accepted Letter of Assurance then the statement is listed on the IeeE-saWebsiteathttp://standards.ieeeorg/about/sasb/patcom/patents.htmlLettersofAssurancemay indicate whether the Submitter is willing or unwilling to grant licenses under patent rights without compensation or under reasonable rates, with reasonable terms and conditions that are demonstrably free of any unfair discrimination to applicants desiring to obtain such licenses Essential Patent Claims may exist for which a Letter of Assurance has not been received The IEee is not responsible for identifying Essential Patent Claims for which a license may be required, for conducting inquiries into the legal validity or scope of Patents Claims, or determining whether any licensing terms or conditions provided in connection with submission of a Letter of Assurance, if any, or in any licensing agreements are reasonable or non-discriminatory. Users of this standard are expressly advised that determination of the validity of any patent rights, and the risk of infringement of such rights, is entirely their own responsibility. Further information may be obtained from the IEEE Standards Association Copyright 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Participants The following participants in the Floating-Point Working Group contributed to the development of this standard David G. Hough, Chair Mike Cowlishaw editor Jonathan bradbury Ivan godard David matula Neil Burgess Roger A. dolliver lan mclntosh David h. c. chen Mrudula gore Richard A. painter Marius cornea Trenton grale Bogdan pasca John h. crawford Michel lack Nathalie revol loe darcy John hauser Jason ricd James demmel Peter C.B. Henderson Eric m. schwarz Florent de dinechin William Kahan James w. thomas Ken docker R. Baker Kearfott Leonard tsai Hossam a.h. fahmy Christoph lauter Fred J. Tydeman Warren E. Ferguson Vincent lefevre Liang-Kai Wang David m. gav David lutz Lee winter Tcrjc Mathison The following individual members of the balloting committee voted on this standard. Balloters might have voted for approval, disapproval, or abstention Robert aiello Randall groves Nick S. A. Nikjoo Amelia Andersdotter Michel lack Richard A painter Israel barrientos Peter harrod John pi Demetrio Bucaneg Jr Chris n. hinds Nathalie revol David h. c. chen Werner hoelzl Jason ried James Cloos David G. Hough Randy saunders Marius cornea Piotr Karocki Eric m. schwarz Mike cowlishaw R. Baker Kearfott James stine James demmel Jim Kulchisky Walter Struppler Ken Docker Christoph lauter James w. thomas Hossam a.h. fahmy Ⅴ incent Lefevre Michael Thompson Andrew fieldsend Edward mccall Leonard tsai David m. gay Jean-Michel Muller Forrest wright H. Glickenste Bruce muschlitz Jian yu Roger A Colliver Ned nedialkov Oren Yuen Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti When the IEEE-SA Standards Board approved this standard on 13 June 2019, it had the following membership Gary Hoffman, Chair Ted Burse Vice Chair Jean-Philippe Faure, Past chair Konstantinos Karachalios, Secretary Masayuki Ariyoshi David. law Annette reilly Stephen D Dukes Joseph levy Dorothy stanley J. Travis griffith Howard li ha w Guido hertz Xiaohui liu Phil Wennblom Christel hunter Kevin lu Philip winston Joseph l. Koepfinger Daleep mohla Howard Wolfman Thomas Koshy Andrew myles Feng w John D. kulick Jingyi Zhou Member emeritus Copyright 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Introduction This introduction is not part of iEEE Std 754-2019, 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 perations specified in the normative part of this standard, numerical results and exceptions are uniquel 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 loating-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 common elementary functions such as exp or 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. Informative annexes provide additional information- Annex a lists bibliographical resources, Annex B suggests programming environment features for debugging support, and Annex C lists all references to the operations of the standard Copyright o 2019 IEEE. All rights reserved IEEE Std 754-2019 IEEE Standard for Floating-Point Arithmeti Contents 1. Overview 1.1 Scope......,.,…1l 1.2 Purpose 1. 3 Inclusions 1. 4 Exclusions 1.5 Programming environment considerations 12 1.6 Word usage… 2. Definitions, abbreviations, and acronyms ∴13 2.1 Definitions.…… 2.2 Abbreviations and acronyms 15 3. Floating-point fo 3.1 Overview 3.2 Specification levels 17 3.3 Sets of floating-point data 17 3. 4 Binary interchange format encodings. 19 3. 5 Decimal interchange format encodings 20 3.6 Interchange format parameters 3.7 Extended and extendable precisions 4. Attributes and rounding 26 4.1 Attribute specification 4.2 Dynamic modes for attributes.…… 26 4.3 Rounding-direction attributes 5. Operations 5.1 Overview 29 5.2 Decimal exponent calculation 30 5.3 Homogeneous general-computational operations 5.4 formatOf general-computational operations 5.5 Quiet-computational operations 5.6 Signaling-computational operations 37 5.7 Non-computational operations 37 5.8 Details of conversions from floating-point to integer formats 39 5.9 Details of operations to round a floating-point datum to integral value 41 5.10 Details of totalOrder predicate .42 5.11 Details of comparison predicates 43 5.12 Details of conversion between floating-point data and external character sequences 44 6. Infinity, NaNs, and sign bit 6. 1 Infinity arithmetic 48 6.2 Operations with NaNs 6.3Th bit 7. Exceptions and default exception handling 7. 1 Overview: exceptions and flags 7.2 Invalid operation...... 52 7.3 Division by zero 740 verflow............. 7.5 Underflow 555 7.6 Inexact 8. Alternate exception handling attributes. 8. 1 Overview 8.2 Resuming alternate exception handling attributes 8.3 Immediate and delayed alternate exception handling attributes 56 9 Copyright 2019 IEEE. All rights reserved 【实例截图】
【核心代码】
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