DOCSLIB.ORG

Arm Fortran Compiler Reference Guide Version 19.1.0

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Arm Fortran Compiler Reference Guide Version 19.1.0 Document Number 101380_1910_00 CONTENTS 1 Overview 3 1.1 Arm Fortran Compiler........................................3 1.2 About this book...........................................3 1.3 Getting help.............................................3 2 Get started 5 2.1 Installation..............................................5 2.2 Configuring environment.......................................5 2.3 Compiling and running a simple “Hello World” program......................6 2.4 Generating executable binaries from Fortran code..........................6 2.5 Compiling and linking object files as separate steps.........................6 2.6 Increasing the optimization level...................................6 2.7 Compiling and optimizing using CPU auto-detection........................7 2.8 Compiling Fortran code for SVE-enabled target architectures...................7 2.9 Common compiler options......................................7 2.10 Get support..............................................8 3 Compiler options 9 3.1 Actions................................................9 3.2 File options..............................................9 3.3 Basic driver options......................................... 10 3.4 Optimization options......................................... 10 3.5 Workload compilation options.................................... 12 3.6 Development options......................................... 14 3.7 Warning options........................................... 14 3.8 Pre-processor options........................................ 14 3.9 Linker options............................................ 15 4 Fortran data types and file extensions 17 4.1 Data types.............................................. 17 4.2 Supported file extensions....................................... 18 4.3 Logical variables and constants................................... 19 4.4 C/Fortran inter-language calling................................... 19 4.5 Character............................................... 20 4.6 Complex............................................... 20 4.7 Arm Fortran Compiler Fortran implementation notes........................ 21 5 Fortran statements 23 5.1 Statements.............................................. 23 6 Fortran intrinsics 31 6.1 Overview............................................... 31 6.2 Bit manipulation functions and subroutines............................. 31 6.3 Elemental character and logical functions.............................. 32 6.4 Vector/Matrix functions....................................... 34 i Document number 101380_1910_00 6.5 Array reduction functions...................................... 34 6.6 String construction functions..................................... 37 6.7 Array construction manipulation functions............................. 37 6.8 General inquiry functions...................................... 38 6.9 Numeric inquiry functions...................................... 39 6.10 Array inquiry functions....................................... 40 6.11 Transfer functions.......................................... 40 6.12 Arithmetic functions......................................... 41 6.13 Miscellaneous functions....................................... 44 6.14 Subroutines.............................................. 45 6.15 Fortran 2003 functions........................................ 45 6.16 Fortran 2008 functions........................................ 46 6.17 Unsupported functions........................................ 48 6.18 Unsupported subroutines....................................... 50 7 Directives 53 7.1 ivdep................................................. 53 7.2 vector always............................................. 54 7.3 novector............................................... 55 7.4 omp simd............................................... 56 7.5 unroll................................................. 57 7.6 nounroll................................................ 58 8 Optimization remarks 61 8.1 Optimization remarks........................................ 61 9 Standards support 63 9.1 Fortran 2003............................................. 63 9.2 Fortran 2008............................................. 65 9.3 OpenMP 4.0............................................. 66 9.4 OpenMP 4.5............................................. 67 10 Further resources 69 10.1 Further resources........................................... 69 Document number 101380_1910_00 ii CONTENTS Arm Fortran Compiler Reference Guide Copyright © [2016-2019], Arm Limited (or its affiliates). All rights reserved. Release information Table 1: Document history Issue Date Confidentiality Change 1830_00 20 June 2018 Non-Confidential 18.3.0 1840_00 27 July 2018 Non-Confidential 18.4.0 1900_00 2 November 2018 Non-Confidential 19.0.0 1910_00 8 March 2019 Non-Confidential 19.1.0 Non-Confidential Proprietary Notice This document is protected by copyright and other related rights and the practice or implementation of the information contained in this document may be protected by one or more patents or pending patent applications. No part of this document may be reproduced in any form by any means without the express prior written permission of Arm. No license, express or implied, by estoppel or otherwise to any intellectual property rights is granted by this document unless specifically stated. Your access to the information in this document is conditional upon your acceptance that you will not use or permit others to use the information for the purposes of determining whether implementations infringe any third party patents. THIS DOCUMENT IS PROVIDED “AS IS”. ARM PROVIDES NO REPRESENTATIONS AND NO WAR- RANTIES, EXPRESS, IMPLIED OR STATUTORY, INCLUDING, WITHOUT LIMITATION, THE IMPLIED WARRANTIES OF MERCHANTABILITY, SATISFACTORY QUALITY, NON-INFRINGEMENT OR FITNESS FOR A PARTICULAR PURPOSE WITH RESPECT TO THE DOCUMENT. For the avoidance of doubt, Arm makes no representation with respect to, and has undertaken no analysis to identify or understand the scope and content of, third party patents, copyrights, trade secrets, or other rights. This document may include technical inaccuracies or typographical errors. TO THE EXTENT NOT PROHIBITED BY LAW, IN NO EVENT WILL ARM BE LIABLE FOR ANY DAM- AGES, INCLUDING WITHOUT LIMITATION ANY DIRECT, INDIRECT, SPECIAL, INCIDENTAL, PUNI- TIVE, OR CONSEQUENTIAL DAMAGES, HOWEVER CAUSED AND REGARDLESS OF THE THEORY OF LIABILITY, ARISING OUT OF ANY USE OF THIS DOCUMENT, EVEN IF Arm HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. This document consists solely of commercial items. You shall be responsible for ensuring that any use, duplication or disclosure of this document complies fully with any relevant export laws and regulations to assure that this document or any portion thereof is not exported, directly or indirectly, in violation of such export laws. Use of the word “partner” in reference to Arm’s customers is not intended to create or refer to any partnership relationship with any other company. Arm may make changes to this document at any time and without notice. If any of the provisions contained in these terms conflict with any of the provisions of any signed written agreement covering this document with Arm, then the signed written agreement prevails over and supersedes the conflicting provisions of these terms. This document may be translated into other languages for convenience, and you agree that if there is any conflict between the English version of this document and any translation, the terms of the English version of the Agreement shall prevail. Words and logos marked with ® or ™ are registered trademarks or trademarks of Arm Limited or its affiliates in the EU and/or elsewhere. All rights reserved. Other brands and names mentioned in this document may be the trademarks of their respective owners. Please follow Arm’s trademark usage guidelines at http://www.arm.com/ about/trademark-usage-guidelines.php Copyright © [2016-2019], Arm Limited (or its affiliates). All rights reserved. Arm Limited. Company 02557590 registered in England. 110 Fulbourn Road, Cambridge, England CB1 9NJ. LES-PRE-20349 Confidentiality Status 1 Document number 101380_1910_00 Arm Fortran Compiler Reference Guide CONTENTS This document is Non-Confidential. The right to use, copy and disclose this document may be subject to license restrictions in accordance with the terms of the agreement entered into by Arm and the party that Arm delivered this document to. Unrestricted Access is an Arm internal classification. Product Status The information in this document is Final, that is for a developed product. Web Address http://www.arm.com Document number 101380_1910_00 2 CHAPTER ONE OVERVIEW Gives an overview of the Arm Fortran Compiler, the information within this book, and provides information on how to get further support. 1.1 Arm Fortran Compiler Arm Fortran Compiler is an auto-vectorizing, Linux user-space Fortran compiler, tailored for High Performance Computing (HPC) and scientific workloads. It is built on the open-source Flang front-end and the LLVM-based optimization and code generation back-end. It supports popular Fortran and OpenMP standards and is tuned for 64-bit Armv8-A architecture. Arm Fortran Compiler is available in combination with Arm C/C++ Compiler, Arm Performance Libraries, Arm Forge, and Arm Performance Reports as part of the Arm Allinea Studio. Arm Allinea Studio is the end-to-end commercial suite for building and porting HPC applications
Recommended publications
  • Nios II Custom Instruction User Guide

    Nios II Custom Instruction User Guide

    Nios II Custom Instruction User Guide Subscribe UG-20286 | 2020.04.27 Send Feedback Latest document on the web: PDF | HTML Contents Contents 1. Nios II Custom Instruction Overview..............................................................................4 1.1. Custom Instruction Implementation......................................................................... 4 1.1.1. Custom Instruction Hardware Implementation............................................... 5 1.1.2. Custom Instruction Software Implementation................................................ 6 2. Custom Instruction Hardware Interface......................................................................... 7 2.1. Custom Instruction Types....................................................................................... 7 2.1.1. Combinational Custom Instructions.............................................................. 8 2.1.2. Multicycle Custom Instructions...................................................................10 2.1.3. Extended Custom Instructions................................................................... 11 2.1.4. Internal Register File Custom Instructions................................................... 13 2.1.5. External Interface Custom Instructions....................................................... 15 3. Custom Instruction Software Interface.........................................................................16 3.1. Custom Instruction Software Examples................................................................... 16
  • The MPFR Team Mpfr@Loria.Fr This Manual Documents How to Install and Use the Multiple Precision Floating-Point Reliable Library, Version 2.2.0

    The MPFR Team [email protected] This Manual Documents How to Install and Use the Multiple Precision Floating-Point Reliable Library, Version 2.2.0

    MPFR The Multiple Precision Floating-Point Reliable Library Edition 2.2.0 September 2005 The MPFR team [email protected] This manual documents how to install and use the Multiple Precision Floating-Point Reliable Library, version 2.2.0. Copyright 1991, 1993, 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2001, 2002, 2003, 2004, 2005 Free Software Foundation, Inc. Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.1 or any later version published by the Free Software Foundation; with no Invariant Sections, with the Front-Cover Texts being “A GNU Manual”, and with the Back-Cover Texts being “You have freedom to copy and modify this GNU Manual, like GNU software”. A copy of the license is included in Appendix A [GNU Free Documentation License], page 30. i Table of Contents MPFR Copying Conditions ................................ 1 1 Introduction to MPFR ................................. 2 1.1 How to use this Manual ........................................................ 2 2 Installing MPFR ....................................... 3 2.1 How to install ................................................................. 3 2.2 Other make targets ............................................................ 3 2.3 Known Build Problems ........................................................ 3 2.4 Getting the Latest Version of MPFR ............................................ 4 3 Reporting Bugs ........................................ 5 4 MPFR Basics .........................................
  • IEEE Std 754-1985 Revision of Reaffirmed1990 IEEE Standard for Binary Floating-Point Arithmetic

    IEEE Std 754-1985 Revision of Reaffirmed1990 IEEE Standard for Binary Floating-Point Arithmetic

    Recognized as an American National Standard (ANSI) IEEE Std 754-1985 An American National Standard IEEE Standard for Binary Floating-Point Arithmetic Sponsor Standards Committee of the IEEE Computer Society Approved March 21, 1985 Reaffirmed December 6, 1990 IEEE Standards Board Approved July 26, 1985 Reaffirmed May 21, 1991 American National Standards Institute © Copyright 1985 by The Institute of Electrical and Electronics Engineers, Inc 345 East 47th Street, New York, NY 10017, USA No part of this publication may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher. IEEE Standards documents are developed within the Technical Committees of the IEEE Societies and the Standards Coordinating Committees of the IEEE Standards Board. Members of the committees serve voluntarily and without compensation. They are not necessarily members of the Institute. The standards developed within IEEE represent a consensus of the broad expertise on the subject within the Institute as well as those activities outside of IEEE which have expressed an interest in participating in the development of the standard. Use of an IEEE Standard is wholly voluntary. The existence of an IEEE Standard does not imply that there are no other ways to produce, test, measure, purchase, market, or provide other goods and services related to the scope of the IEEE Standard. Furthermore, the viewpoint expressed at the time a standard is approved and issued is subject to change brought about through developments in the state of the art and comments received from users of the standard. Every IEEE Standard is subjected to review at least once every five years for revision or reaffirmation.
  • FORTRAN 77 Language Reference

    FORTRAN 77 Language Reference

    FORTRAN 77 Language Reference FORTRAN 77 Version 5.0 901 San Antonio Road Palo Alto, , CA 94303-4900 USA 650 960-1300 fax 650 969-9131 Part No: 805-4939 Revision A, February 1999 Copyright Copyright 1999 Sun Microsystems, Inc. 901 San Antonio Road, Palo Alto, California 94303-4900 U.S.A. All rights reserved. All rights reserved. This product or document is protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation. No part of this product or document may be reproduced in any form by any means without prior written authorization of Sun and its licensors, if any. Portions of this product may be derived from the UNIX® system, licensed from Novell, Inc., and from the Berkeley 4.3 BSD system, licensed from the University of California. UNIX is a registered trademark in the United States and in other countries and is exclusively licensed by X/Open Company Ltd. Third-party software, including font technology in this product, is protected by copyright and licensed from Sun’s suppliers. RESTRICTED RIGHTS: Use, duplication, or disclosure by the U.S. Government is subject to restrictions of FAR 52.227-14(g)(2)(6/87) and FAR 52.227-19(6/87), or DFAR 252.227-7015(b)(6/95) and DFAR 227.7202-3(a). Sun, Sun Microsystems, the Sun logo, SunDocs, SunExpress, Solaris, Sun Performance Library, Sun Performance WorkShop, Sun Visual WorkShop, Sun WorkShop, and Sun WorkShop Professional are trademarks or registered trademarks of Sun Microsystems, Inc. in the United States and in other countries.
  • Languages Fortran 90 and C / C+--L

    Languages Fortran 90 and C / C+--L

    On the need for predictable floating-point arithmetic in the programming languages Fortran 90 and C / C+--l- DENNIS VERSCHAEREN, ANNIE CUYT AND BRIGITTE VERDONK University of Antwerp (Campus UIA) InfoProc Department of Mathematics and Computer Science Universiteitsplein 1 B-2610 Antwerp - Belgium E-mail: Dennis. Yerschaeren~uia. ua. ac. be E-mail: Annie. Cuyt@uia. ua. ac. be E-mail: Brigitte. Verdonk~uia. ua. ac. be Abstract. During the past decade the IEEE 754 standard for binary floating-point arithmetic has been very successful. Many of today's hardware platforms conform to this standard and compilers should make floating-point functionality available to programmers through high-level programming languages. They should also implement certain features of the IEEE 754 standard in software, such as the input and output conversions to and from the internal binary representation of numbers. In this report, a number of Fortran 90 and C / C++ compilers for workstations as well as personal computers will be screened with respect to their IEEE conformance. It will be shown that most of these compilers do not conform to the IEEE standard and that shortcomings are essentially due to their respective programming language standards which lack attention for the need of predictable floating-point arithmetic. Categories and subject descriptors: G.1.0 [Numerical Analysis]: General--Computer arithmetic; D.3.0 [Programming Languages]: General--Standards; D.3.4 [Programming Languages]: Processors--Compilers AMS subject classifications: 68N15, 68N20 General terms: floating-point, arithmetic Additional key words and phrases: IEEE floating-point standard, Fortran 90, C, C++ 1 - Introduction The IEEE standard for floating-point arithmetic describes how floating-point numbers should be handled in hardware and software.
  • Beal's Conjecture Vs. "Positive Zero", Fight

    Beal's Conjecture Vs. "Positive Zero", Fight

    Beal's Conjecture vs. "Positive Zero", Fight By Angela N. Moore Yale University [email protected] January 6, 2015 Abstract This article seeks to encourage a mathematical dialog regarding a possible solution to Beal’s Conjecture. It breaks down one of the world’s most difficult math problems into layman’s terms and encourages people to question some of the most fundamental rules of mathematics. More specifically; it reinforces basic algebra/critical thinking skills, makes use of properties attributed to the number one and reanalyzes the definition of a positive integer in order to provide a potential counterexample to Beal's Conjecture. I. THE UNDEFEATED CHAMPION (BEAL’S CONJECTURE) A^x + B^y = C^z Where A, B, C, x, y, and z are positive integers with x, y, z > 2, then A, B, and C have a common prime factor. II. NOW FOR THE COUNTEREXAMPLE OF DOOM Pre-Fight: Beal’s Conjecture is never true when (A^x= 1) + B^y = C^z. This is because 1 has no prime factors. Let the Games Begin: There are instances when positive 0 is not the same as zero. “Signed zero is zero with an associated sign. In ordinary arithmetic, −0 = +0 = 0. However, in computing, some number representations allow for the existence of two zeros, often denoted by −0 (negative zero) and +0 (positive zero).”i Furthermore, the same website proved that signed 0 sometimes produces different results than 0. “…the concept of signed zero runs contrary to the general assumption made in most mathematical fields (and in most mathematics courses) that negative zero is the same thing as zero.
  • Numerical Computation Guide

    Numerical Computation Guide

    Numerical Computation Guide A Sun Microsystems, Inc. Business 2550 Garcia Avenue Mountain View, CA 94043 U.S.A. Part No.: 801-7639-10 Revision A, August 1994 1994 Sun Microsystems, Inc. 2550 Garcia Avenue, Mountain View, California 94043-1100 U.S.A. All rights reserved. This product and related documentation are protected by copyright and distributed under licenses restricting its use, copying, distribution, and decompilation. No part of this product or related documentation may be reproduced in any form by any means without prior written authorization of Sun and its licensors, if any. Portions of this product may be derived from the UNIX® and Berkeley 4.3 BSD systems, licensed from UNIX System Laboratories, Inc., a wholly owned subsidiary of Novell, Inc., and the University of California, respectively. Third-party font software in this product is protected by copyright and licensed from Sun’s font suppliers. RESTRICTED RIGHTS LEGEND: Use, duplication, or disclosure by the United States Government is subject to the restrictions set forth in DFARS 252.227-7013 (c)(1)(ii) and FAR 52.227-19. The product described in this manual may be protected by one or more U.S. patents, foreign patents, or pending applications. TRADEMARKS Sun, the Sun logo, Sun Microsystems, Sun Microsystems Computer Corporation, Solaris, are trademarks or registered trademarks of Sun Microsystems, Inc. in the U.S. and certain other countries. UNIX is a registered trademark of Novell, Inc., in the United States and other countries; X/Open Company, Ltd., is the exclusive licensor of such trademark. OPEN LOOK® is a registered trademark of Novell, Inc.
  • Floating Point

    Floating Point

    Contents Articles Floating point 1 Positional notation 22 References Article Sources and Contributors 32 Image Sources, Licenses and Contributors 33 Article Licenses License 34 Floating point 1 Floating point In computing, floating point describes a method of representing an approximation of a real number in a way that can support a wide range of values. The numbers are, in general, represented approximately to a fixed number of significant digits (the significand) and scaled using an exponent. The base for the scaling is normally 2, 10 or 16. The typical number that can be represented exactly is of the form: Significant digits × baseexponent The idea of floating-point representation over intrinsically integer fixed-point numbers, which consist purely of significand, is that An early electromechanical programmable computer, expanding it with the exponent component achieves greater range. the Z3, included floating-point arithmetic (replica on display at Deutsches Museum in Munich). For instance, to represent large values, e.g. distances between galaxies, there is no need to keep all 39 decimal places down to femtometre-resolution (employed in particle physics). Assuming that the best resolution is in light years, only the 9 most significant decimal digits matter, whereas the remaining 30 digits carry pure noise, and thus can be safely dropped. This represents a savings of 100 bits of computer data storage. Instead of these 100 bits, much fewer are used to represent the scale (the exponent), e.g. 8 bits or 2 A diagram showing a representation of a decimal decimal digits. Given that one number can encode both astronomic floating-point number using a mantissa and an and subatomic distances with the same nine digits of accuracy, but exponent.
  • 5.3.1 Min and Max Operations

    5.3.1 Min and Max Operations

    The Removal/Demotion of MinNum and MaxNum Operations from IEEE 754™-2018 David H.C. Chen February 21, 2017 Acknowledgements In writing this report, I received help from many colleagues. A thank you to all my colleagues from Floating-Point Working Group for providing crucial insights and expertise. I would also like to express special appreciation to Bob Alverson, Steve Canon, Mike Cowlishaw, David Gay, Michel Hack, John Hauser, David Hough, William Huffman, Grant Martin, Terje Mathisen, Jason Riedy, and Lee Winter, whose valuable inputs, suggestions and comments have significantly improved this report. Any errors or omissions are mine and should not reflect on my colleagues. 1 Introduction IEEE Standard for Floating-Point Arithmetic 754™ 2008 version (IEEE std 754™-2008) [6] specifies four minimum and maximum (min-max) operations: minNum, maxNum, minNumMag, and maxNumMag, in sub-clause “5.3.1 General operations”. These four min-max operations are removed from or demoted in IEEE std 754™-2018 [7], due to their non-associativity. No existing implementations become non-conformant due to this removal/demotion. This report explains the technical reasons for the removal/demotion of the above four min-max operations, and reviews existing min-max implementations in some programming language standards and commercial hardware. Many implementations support several floating-point formats, but this report will only present one or two selected formats for an implementation when additional formats are supported in the same way. To be brief, this report focuses on treatments of Not a Number (NaN) by max operations. A given implementation may also provide max magnitude, min, and min magnitude operations treating signaling NaN (sNaN) and quiet NaN (qNaN) in the same way.
  • New Directions in Floating-Point Arithmetic

    New Directions in Floating-Point Arithmetic

    New directions in floating-point arithmetic Nelson H. F. Beebe University of Utah Department of Mathematics, 110 LCB 155 S 1400 E RM 233 Salt Lake City, UT 84112-0090 USA Abstract. This article briefly describes the history of floating-point arithmetic, the development and features of IEEE standards for such arithmetic, desirable features of new implementations of floating-point hardware, and discusses work- in-progress aimed at making decimal floating-point arithmetic widely available across many architectures, operating systems, and programming languages. Keywords: binary arithmetic; decimal arithmetic; elementary functions; fixed-point arithmetic; floating-point arithmetic; interval arithmetic; mathcw library; range arithmetic; special functions; validated numerics PACS: 02.30.Gp Special functions DEDICATION This article is dedicated to N. Yngve Öhrn, my mentor, thesis co-advisor, and long-time friend, on the occasion of his retirement from academia. It is also dedicated to William Kahan, Michael Cowlishaw, and the late James Wilkinson, with much thanks for inspiration. WHAT IS FLOATING-POINT ARITHMETIC? Floating-point arithmetic is a technique for storing and operating on numbers in a computer where the base, range, and precision of the number system are usually fixed by the computer design. Conceptually, a floating-point number has a sign,anexponent,andasignificand (the older term mantissa is now deprecated), allowing a representation of the form .1/sign significand baseexponent.Thebase point in the significand may be at the left, or after the first digit, or at the right. The point and the base are implicit in the representation: neither is stored. The sign can be compactly represented by a single bit, and the exponent is most commonly a biased unsigned bitfield, although some historical architectures used a separate exponent sign and an unbiased exponent.
  • Catalogue of Common Sorts of Bug

    Catalogue of Common Sorts of Bug

    Warwick Research Software Engineering Catalogue of Common Sorts of Bug H. Ratcliffe and C.S. Brady Senior Research Software Engineers \The Angry Penguin", used under creative commons licence from Swantje Hess and Jannis Pohlmann. October 2, 2018 1 Bug Catalogue 1.1 Logic or algorithm bugs Logic bugs are a catch-all for when your program does what it ought to, but not what you wanted; effectively you have written the wrong correct program. They can be very tricky to find, because they often arise from some misunderstanding of what you are trying to achieve. You may find it helpful to look over your plan (you did make a plan, right?) Symptoms: • incorrect answers • poor performance Examples: • Finding the minimum of a list the wrong way: if your data is sorted, the minimum value must be the first in the list but sorting the data to just find the minimum item is silly.1 • Missing parts of a range: 1 INTEGER a , c 2 a = GET NEXT INTEGER( ) 3 IF ( a < 0 ) THEN 4 c = 1 5 ELSE IF ( a > 0 AND a < 5) THEN 6 c = 0 7 ELSE IF ( a >= 5) THEN 8 c = 2 9 END Notice that the case of a == 0 has been missed, and in this case c is undefined. • Single branch of sqrt: calculating a from something like a2 = 9, and forgetting that a can be either 3 or -3, introducing a sign error in further calculations • Most typos: mistyped names, function assignment rather than call (Python), missing semicolon (C). Mis-use of operators, for example using & and && (C).
  • Study of the Posit Number System: a Practical Approach

    Study of the Posit Number System: a Practical Approach

    STUDY OF THE POSIT NUMBER SYSTEM: A PRACTICAL APPROACH Raúl Murillo Montero DOBLE GRADO EN INGENIERÍA INFORMÁTICA – MATEMÁTICAS FACULTAD DE INFORMÁTICA UNIVERSIDAD COMPLUTENSE DE MADRID Trabajo Fin Grado en Ingeniería Informática – Matemáticas Curso 2018-2019 Directores: Alberto Antonio del Barrio García Guillermo Botella Juan Este documento está preparado para ser imprimido a doble cara. STUDY OF THE POSIT NUMBER SYSTEM: A PRACTICAL APPROACH Raúl Murillo Montero DOUBLE DEGREE IN COMPUTER SCIENCE – MATHEMATICS FACULTY OF COMPUTER SCIENCE COMPLUTENSE UNIVERSITY OF MADRID Bachelor’s Degree Final Project in Computer Science – Mathematics Academic year 2018-2019 Directors: Alberto Antonio del Barrio García Guillermo Botella Juan To me, mathematics, computer science, and the arts are insanely related. They’re all creative expressions. Sebastian Thrun Acknowledgements I have to start by thanking Alberto Antonio del Barrio García and Guillermo Botella Juan, the directors of this amazing project. Thank you for this opportunity, for your support, your help and for trusting me. Without you any of this would have ever been possible. Thanks to my family, who has always supported me and taught me that I am only limited by the limits I choose to put on myself. Finally, thanks to all of you who have accompanied me on this 5 year journey. Sharing classes, exams, comings and goings between the two faculties with you has been a wonderful experience I will always remember. vii Abstract The IEEE Standard for Floating-Point Arithmetic (IEEE 754) has been for decades the standard for floating-point arithmetic and is implemented in a vast majority of modern computer systems.