ISO/IEC INTERNATIONAL STANDARD 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 I'information Arithmétique independante des langages Partie 3: Arithmetique des nombres complexes entiers et en virgule flottante et fonctions numériques élémentaires complexes Reference number ISO/IEC 10967-3:2006(E) IEC ISo @ISO/IEC2006 ISO/IEC 10967-3:2006(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The Iso Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Detais of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by IsO member bodies. In ? ISO/IEC2006 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 mechanical, including photocopying and microfilm, without permission in writing from either isO at the address below or IsO's 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 [email protected] Web www.iso.org Published in Switzerland @ ISO/IEC 2006 - All rights reserved ISO/IEC 10967-3:2006(E) Contents Foreword vii Introduction viii 1 Scope 1 1.1 Inclusions 1 1.2 Exclusions 2 2 Conformity 3 3 Normative references 4 Symbols and definitions 4 4.1 Symbols 4 4.1.1 Sets and intervals . 4 4.1.2 Operators and relations 4 4.1.3 Mathematical functions 5 4.1.4 Exceptional values 6 4.1.5 Datatypes and special values 6 4.1.6 Complex value constructors and complex datatype constructors 8 4.2 Definitions of terms . 9 Specifications for imaginary and complex datatypes and operations 14 5.1 Imaginary and complex integer datatypes and operations 14 5.1.1 The complex integer result helper function 15 5.1.2 Imaginary and complex integer operations 15 5.1.2.1 Complex integer comparisons 15 5.1.2.2 Multiplication by the imaginary unit . 17 5.1.2.3 The real and imaginary parts of a complex value 17 5.1.2.4 Formation of a complex integer from two real valued integers 18 5.1.2.5 Basic complex integer arithmetic . 18 5.1.2.6 Absolute value and signum of integers and imaginary integers . 21 5.1.2.7 Divisibility interrogation 21 5.1.2.8 Integer division and remainder extended to imaginary and complex integers 22 5.1.2.9 Maximum and minimum 27 5.2 Imaginary and complex floating point datatypes and operations 28 5.2.1 Maximum error requirements 28 5.2.2 Sign requirements 29 5.2.3 Monotonicity requirements 30 5.2.4 The complex floating point result helper functions 30 5.2.5 Basic arithmetic for complex floating point 31 5.2.5.1 Complex floating point comparisons 31 5.2.5.2 Multiplication by the imaginary unit 33 5.2.5.3 The real and imaginary parts of a complex value 34 5.2.5.4 Formation of a complex floating point from two floating point values 34 5.2.5.5 Fundamental complex floating point arithmetic 34 stion All rights reserved ili ISO/IEC 10967-3:2006(E) 5.2.5.6 Absolute value, phase and signum of complex floating point values 38 5.2.5.7 Floor, round, and ceiling 39 5.2.5.8 Maximum and minimum 39 5.2.6 Complex sign, multiplication, and division 40 5.2.6.1 Complex signum 41 5.2.6.2 Complex multiplication 41 5.2.6.3 Complex division . 42 5.2.7 Operations for conversion from polar to Cartesian 43 5.3 Elementary transcendental imaginary an