ISO_IEC_10967-3_2006E.pdf

Reference numberISO/IEC 10967-3:2006(E)ISO/IEC 2006 INTERNATIONAL STANDARD ISO/IEC10967-3First edition2006-05-01Information technology Language independent arithmetic Part 3:Complex integer and floating point arithmetic and complex elementary numerical functions Technologies de linformation Arithmtique indpendante des langages Partie 3:Arithmtique des nombres complexes entiers et en virgule flottante et fonctions numriques lmentaires complexes 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 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 Adobes 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 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 mechanical,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.iso.org Published in Switzerland ii ISO/IEC 2006 All rights reserved ISO/IEC 10967-3:2006(E)ISO/IEC 2006 All rights reserved iii ContentsForewordviiIntroductionviii1Scope11.1Inclusions.11.2Exclusions.22Conformity33Normative references44Symbols and definitions44.1Symbols.44.1.1Sets and intervals.44.1.2Operators and relations.44.1.3Mathematical functions.54.1.4Exceptional values.64.1.5Datatypes and special values.64.1.6Complex value constructors and complex datatype constructors.84.2Definitions of terms.95Specifications for imaginary and complex datatypes and operations145.1Imaginary and complex integer datatypes and operations.145.1.1The complex integer result helper function.155.1.2Imaginary and complex integer operations.155.1.2.1Complex integer comparisons.155.1.2.2Multiplication by the imaginary unit.175.1.2.3The real and imaginary parts of a complex value.175.1.2.4Formation of a complex integer from two real valued integers.185.1.2.5Basic complex integer arithmetic.185.1.2.6Absolute value and signum of integers and imaginary integers.215.1.2.7Divisibility interrogation.215.1.2.8Integer division and remainder extended to imaginary and complexintegers.225.1.2.9Maximum and minimum.275.2Imaginary and complex floating point datatypes and operations.285.2.1Maximum error requirements.285.2.2Sign requirements.295.2.3Monotonicity requirements.305.2.4The complex floating point result helper functions.305.2.5Basic arithmetic for complex floating point.315.2.5.1Complex floating point comparisons.315.2.5.2Multiplication by the imaginary unit.335.2.5.3The real and imaginary parts of a complex value.345.2.5.4Formation of a complex floating point from two floating point values 345.2.5.5Fundamental complex floating point arithmetic.34ISO/IEC 10967-3:2006(E)iv ISO/IEC 2006 All rights reserved 5.2.5.6Absolute value,phase and signum of complex floating point values385.2.5.7Floor,round,and ceiling.395.2.5.8Maximum and minimum.395.2.6Complex sign,multiplication,and division.405.2.6.1Complex signum.415.2.6.2Complex multiplication.415.2.6.3Complex division.425.2.7Operations for conversion from polar to Cartesian.435.3Elementary transcendental imaginary and complex floating point operations.445.3.1Operations for exponentiations and logarithms.445.3.1.1Exponentiation of imaginary base to integer power.445.3.1.2Natural exponentiation.455.3.1.3Complex exponentiation of argument base.455.3.1.4Complex square root.465.3.1.5Natural logarithm.475.3.2Operations for radian trigonometric elementary functions.495.3.2.1Radian angle normalisation.495.3.2.2Radian sine.495.3.2.3Radian cosine.505.3.2.4Radian tangent.505.3.2.5Radian cotangent.515.3.2.6Radian secant.525.3.2.7Radian cosecant.525.3.2.8Radian arc sine.535.3.2.9Radian arc cosine.545.3.2.10 Radian arc tangent.565.3.2.11 Radian arc cotangent.575.3.2.12 Radian arc secant.585.3.2.13 Radian arc cosecant.595.3.3Operations for hyperbolic elementary functions.605.3.3.1Hyperbolic normalisation.615.3.3.2Hyperbolic sine.615.3.3.3Hyperbolic cosine.615.3.3.4Hyperbolic tangent.615.3.3.5Hyperbolic cotangent.625.3.3.6Hyperbolic secant.625.3.3.7Hyperbolic cosecant.625.3.3.8Inverse hyperbolic sine.625.3.3.9Inverse hyperbolic c