ISO-10967-3-2006.pdf
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1、 Reference number ISO/IEC 10967-3:2006(E) ISO/IEC 2006 INTERNATIONAL STANDARD ISO/IEC 10967-3 First edition 2006-05-01 Information technology Language independent arithmetic Part 3: Complex integer and floating point arithmetic and complex elementary numerical functions Technologies de linformation
2、Arithmtique indpendante des langages Partie 3: Arithmtique des nombres complexes entiers et en virgule flottante et fonctions numriques lmentaires complexes Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=IHS Employees/1111111001, User=Wing, B
3、ernie Not for Resale, 04/03/2007 02:14:16 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO/IEC 10967-3:2006(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobes licensing policy, this file may be printed or viewed but shall not be edi
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6、dies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. ISO/IEC 2006 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mec
7、hanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISOs member body in the country of the requester. ISO copyright office Case postale 56 CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyrightiso.org Web www.i
8、so.org Published in Switzerland ii ISO/IEC 2006 All rights reserved Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale, 04/03/2007 02:14:16 MDTNo reproduction or networking permitted with
9、out license from IHS -,-,- ISO/IEC 10967-3:2006(E) ISO/IEC 2006 All rights reserved iii Contents Forewordvii Introductionviii 1Scope1 1.1Inclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1 1.2Exclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . .
10、 . . . . . . . . . . . . .2 2Conformity3 3Normative references4 4 Symbols and defi nitions4 4.1Symbols . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 4.1.1Sets and intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 4.1.2Operators and re
11、lations . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4 4.1.3Mathematical functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 4.1.4Exceptional values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 4.1.5Datatypes and special values. . . . . . . . . . . .
12、. . . . . . . . . . . . . .6 4.1.6Complex value constructors and complex datatype constructors . . . . . . .8 4.2 Defi nitions of terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 5 Specifi cations for imaginary and complex datatypes and operations14 5.1Imaginary and com
13、plex integer datatypes and operations. . . . . . . . . . . . . .14 5.1.1The complex integer result helper function. . . . . . . . . . . . . . . . . .15 5.1.2Imaginary and complex integer operations . . . . . . . . . . . . . . . . . . .15 5.1.2.1Complex integer comparisons . . . . . . . . . . . . . .
14、 . . . . . . .15 5.1.2.2Multiplication by the imaginary unit . . . . . . . . . . . . . . . . .17 5.1.2.3The real and imaginary parts of a complex value . . . . . . . . . .17 5.1.2.4Formation of a complex integer from two real valued integers . . .18 5.1.2.5Basic complex integer arithmetic . . . . .
15、. . . . . . . . . . . . . .18 5.1.2.6Absolute value and signum of integers and imaginary integers . . .21 5.1.2.7Divisibility interrogation. . . . . . . . . . . . . . . . . . . . . . .21 5.1.2.8Integer division and remainder extended to imaginary and complex integers . . . . . . . . . . . . . . . .
16、. . . . . . . . . . . . . . . . .22 5.1.2.9Maximum and minimum. . . . . . . . . . . . . . . . . . . . . . .27 5.2 Imaginary and complex fl oating point datatypes and operations . . . . . . . . . . .28 5.2.1Maximum error requirements . . . . . . . . . . . . . . . . . . . . . . . . . .28 5.2.2Sign req
17、uirements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .29 5.2.3Monotonicity requirements. . . . . . . . . . . . . . . . . . . . . . . . . . .30 5.2.4 The complex fl oating point result helper functions . . . . . . . . . . . . . .30 5.2.5 Basic arithmetic for complex fl oating point.
18、 . . . . . . . . . . . . . . . . .31 5.2.5.1 Complex fl oating point comparisons . . . . . . . . . . . . . . . . .31 5.2.5.2Multiplication by the imaginary unit . . . . . . . . . . . . . . . . .33 5.2.5.3The real and imaginary parts of a complex value . . . . . . . . . .34 5.2.5.4 Formation of a com
19、plex fl oating point from two fl oating point values 34 5.2.5.5 Fundamental complex fl oating point arithmetic . . . . . . . . . . .34 Copyright International Organization for Standardization Provided by IHS under license with ISO Licensee=IHS Employees/1111111001, User=Wing, Bernie Not for Resale,
20、04/03/2007 02:14:16 MDTNo reproduction or networking permitted without license from IHS -,-,- ISO/IEC 10967-3:2006(E) iv ISO/IEC 2006 All rights reserved 5.2.5.6 Absolute value, phase and signum of complex fl oating point values38 5.2.5.7Floor, round, and ceiling. . . . . . . . . . . . . . . . . . .
21、 . . . .39 5.2.5.8Maximum and minimum. . . . . . . . . . . . . . . . . . . . . . .39 5.2.6Complex sign, multiplication, and division . . . . . . . . . . . . . . . . . . .40 5.2.6.1Complex signum . . . . . . . . . . . . . . . . . . . . . . . . . . . .41 5.2.6.2Complex multiplication . . . . . . . . .
22、 . . . . . . . . . . . . . . .41 5.2.6.3Complex division . . . . . . . . . . . . . . . . . . . . . . . . . . . .42 5.2.7Operations for conversion from polar to Cartesian. . . . . . . . . . . . . .43 5.3 Elementary transcendental imaginary and complex fl oating point operations . . . .44 5.3.1Operati
23、ons for exponentiations and logarithms. . . . . . . . . . . . . . . .44 5.3.1.1Exponentiation of imaginary base to integer power . . . . . . . . .44 5.3.1.2Natural exponentiation . . . . . . . . . . . . . . . . . . . . . . . .45 5.3.1.3Complex exponentiation of argument base. . . . . . . . . . . . .
24、45 5.3.1.4Complex square root. . . . . . . . . . . . . . . . . . . . . . . . .46 5.3.1.5Natural logarithm . . . . . . . . . . . . . . . . . . . . . . . . . . .47 5.3.2Operations for radian trigonometric elementary functions. . . . . . . . . .49 5.3.2.1Radian angle normalisation . . . . . . . . . . .
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