ISO/IEC INTERNATIONAL STANDARD 10967-2 First edition 2001-08-15 Information technology Language independent arithmetic - Part 2: Elementary numerical functions Technologies de I'information Arithmétique de langage independant - Partie 2:Fonctions numériques élémentaires Reference number ISO/IEC 10967-2:2001(E) E( @ISO/IEC 2001 Copyright International Organization for Standardization Not for Resale ISO/IEC 10967-2:2001(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 Details 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 the unlikely event ?ISO/IEC2001 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.ch Printed in Switzerland yemainagazainandardizato @ISO/IEC2001-All rightsreserved networking permitted without license from IHS Not for Resale ISO/IEC 10967-2:2001(E) @ ISO/IEC 2001 - All rights reserved Contents Foreword vili Introduction ix 1 Scope 1 1.1 Inclusions 1 1.2 Exclusions 2 2 Conformity 2 3 Normative references 3 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 5 4.1.5 Datatypes 6 4.2 Definitions of terms 7 5 Specifications for integer and floating point operations 10 5.1 Basic integer operations 10 5.1.1 The integer result and wrap helper functions 10 5.1.2 Integer maximum and minimum 11 5.1.3 Integer diminish 11 5.1.4 Integer power and arithmetic shift 12 5.1.5 Integer square root 12 5.1.6 Divisibility tests 12 5.1.7 Integer division (with foor, round, or ceiling) and remainder 13 5.1.8 Greatest common divisor and least common positive multiple 13 5.1.9 Support operations for extended integer range . 14 5.2 Basic floating point operations 15 5.2.1 The rounding and floating point result helper functions 15 5.2.2 Floating point maximum and minimum 17 5.2.3 Floating point diminish 18 5.2.4 Floor, round, and ceiling . 19 5.2.5 Remainder after division with round to integer 20 5.2.6 Square root and reciprocal square root . 20 5.2.7 Multiplication to higher precision foating point datatype 20 5.2.8 Support operations for extended floating point precision 21 5.3 Elementary transcendental foating point operations 22 5.3.1 Maximum error requirements 22 5.3.2 Sign requirements 23 5.3.3 Monotonicity requirements 23 5.3.4 The result* helper function 23 5.3.5 Hypotenuse 24 5.3.6 Operations for exponentiations and logarithms 24 ii Copyright International Organization for Standardization Not for Resale ISO/IEC 10967-2:2001(E) @ ISO/IEC 2001 - All rights reserved 5.3.6.1 Integer power of argument base 24 5.3.6.2 Natural exponentiation . . 25 5.3.6.3 Natural exponentiation, minus one . 26 5.3.6.4 Exponentiation of 2 27 5.3.6.5 Exponentiation of 10 27 5.3.6.6 Exponentiation of argument base 28 5.3.6.7 Exponentiation of one plus the argument base, minus one 29 5.3.6.8 Natural logarithm 29 5.3.6.9 Natural logarithm of one plus the argument 30 5.3.6.10 2-logarithm