ISO_IEC_10967-2_2001E.pdf

Reference numberISO/IEC 10967-2:2001(E)ISO/IEC 2001INTERNATIONALSTANDARDISO/IEC10967-2First edition2001-08-15Information technology Languageindependent arithmetic Part 2:Elementary numerical functionsTechnologies de linformation Arithmtique de langage indpendant Partie 2:Fonctions numriques lmentairesISO/IEC 10967-2:2001(E)PDF disclaimerThis PDF file may contain embedded typefaces.In accordance with Adobes licensing policy,this file may be printed or viewed but shall notbe edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing.In downloading thisfile,parties accept therein the responsibility of not infringing Adobes licensing policy.The ISO Central Secretariat accepts no liability in thisarea.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 parameterswere optimized for printing.Every care has been taken to ensure that the file is suitable for use by ISO member bodies.In the unlikely eventthat a problem relating to it is found,please inform the Central Secretariat at the address given below.ISO/IEC 2001All rights reserved.Unless otherwise specified,no part of this publication may be reproduced or utilized in any form or by any means,electronicor mechanical,including photocopying and microfilm,without permission in writing from either ISO at the address below or ISOs member bodyin the country of the requester.ISO copyright officeCase postale 56?CH-1211 Geneva 20Tel.+41 22 749 01 11Fax+41 22 749 09 47E-mail copyrightiso.chWeb www.iso.chPrinted in Switzerlandii ISO/IEC 2001 All rights reservedc?ISO/IEC 2001 All rights reservedISO/IEC 10967-2:2001(E)ContentsForeword.viiiIntroduction.ix1Scope11.1Inclusions.11.2Exclusions.22Conformity23Normative references34Symbols and definitions44.1Symbols.44.1.1Sets and intervals.44.1.2Operators and relations.44.1.3Mathematical functions.54.1.4Exceptional values.54.1.5Datatypes.64.2Definitions of terms.75Specifications for integer and floating point operations105.1Basic integer operations.105.1.1The integer result and wrap helper functions.105.1.2Integer maximum and minimum.115.1.3Integer diminish.115.1.4Integer power and arithmetic shift.125.1.5Integer square root.125.1.6Divisibility tests.125.1.7Integer division(with floor,round,or ceiling)and remainder.135.1.8Greatest common divisor and least common positive multiple.135.1.9Support operations for extended integer range.145.2Basic floating point operations.155.2.1The rounding and floating point result helper functions.155.2.2Floating point maximum and minimum.175.2.3Floating point diminish.185.2.4Floor,round,and ceiling.195.2.5Remainder after division with round to integer.205.2.6Square root and reciprocal square root.205.2.7Multiplication to higher precision floating point datatype.205.2.8Support operations for extended floating point precision.215.3Elementary transcendental floating point operations.225.3.1Maximum error requirements.225.3.2Sign requirements.235.3.3Monotonicity requirements.235.3.4The resulthelper function.235.3.5Hypotenuse.245.3.6Operations for exponentiations and logarithms.24iiiISO/IEC 10967-2:2001(E)c?ISO/IEC 2001 All rights reserved5.3.6.1Integer power of argument base.245.3.6.2Natural exponentiation.255.3.6.3Natural exponentiation,minus one.265.3.6.4Exponentiation of 2.275.3.6.5Exponentiation of 10.275.3.6.6Exponentiation of argument base.285.3.6.7Exponentiation of one plus the argument base,minus one.295.3.6.8Natural logarithm.295.3.6.9Natural logarithm of one plus the argument.305.3.6.10 2-logarithm.305.3.6.11 10-logarithm.315.3.6.12 Argument base logarithm.315.3.6.13 Argument base logarithm of one plus each argument.325.3.7Introduction to operations for trigonometric elementary functions.325.3.8Operations for radian trigonometric elementary functions.335.3.8.1Radian angle normalisation.345.3.8.2Radian sine.355.3.8.3Radian cosine.355.3.8.4Radian tangent.365.3.8.5Radian cotangent.365.3.8.6Radian secant.375.3.8.7Radian cosecant.375.3.8.8Radian cosine with sine.385.3.8.9Radian arc sine.385.3.8.10 Radian arc cosine.385.3.8.11 Radian arc tangent.395.3.8.12 Radian arc cotangent.405.3.8.13 Radian arc secant.415.3.8.14 Radian arc cosecant.415.3.8.15 Radian angle from Cartesian co-ordinates.425.3.9Operations for trigonometrics with given angular unit.435.3.9.1Argument angular-unit angle normalisation.435.3.9.2Argument angular-unit sine.445.3.9.3Argument angular-unit cosine.455.3.9.4Argument angular-unit tangent.455.3.9.5Argument angular-unit cotangent.465.3.9.6Argument angular-unit secant.475.3.9.7Argument angular-unit cosecant.475.3.9.8Argument angular-unit cosine with sine.485.3.9.9Argument angular-unit arc sine.485.3.9.10 Argument angular-unit arc cosine.485.3.9.11 Argument angular-unit arc tangent.495.3.9.12 Argument angular-unit arc cotangent.505.3.9.13 Argument angular-unit arc secant.515.3.9.14 Argument angula