Absoft Fortran Language Reference Manual

Total Page:16

File Type:pdf, Size:1020Kb

Absoft Fortran Language Reference Manual i Absoft Fortran Language Reference Manual Absoft Fortran Language Reference Manual 2781 Bond Street Rochester Hills, MI 48309 U.S.A. Tel (248) 853-0095 Fax (248) 853-0108 [email protected] i All rights reserved. No part of this publication may be reproduced or used in any form by any means, without the prior written permission of Absoft Corporation. THE INFORMATION CONTAINED IN THIS PUBLICATION IS BELIEVED TO BE ACCURATE AND RELIABLE. HOWEVER, ABSOFT CORPORATION MAKES NO REPRESENTATION OF WARRANTIES WITH RESPECT TO THE PROGRAM MATERIAL DESCRIBED HEREIN AND SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. FURTHER, ABSOFT RESERVES THE RIGHT TO REVISE THE PROGRAM MATERIAL AND MAKE CHANGES THEREIN FROM TIME TO TIME WITHOUT OBLIGATION TO NOTIFY THE PURCHASER OF THE REVISION OR CHANGES. IN NO EVENT SHALL ABSOFT BE LIABLE FOR ANY INCIDENTAL, INDIRECT, SPECIAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE PURCHASER'S USE OF THE PROGRAM MATERIAL. U.S. GOVERNMENT RESTRICTED RIGHTS — The software and documentation are provided with RESTRICTED RIGHTS. Use, duplication, or disclosure by the Government is subject to restrictions set forth in subparagraph (c) (1) (ii) of the Rights in Technical Data and Computer Software clause at 252.227-7013. The contractor is Absoft Corporation, 2781 Bond Street, Rochester Hills, Michigan 48309. ABSOFT CORPORATION AND ITS LICENSOR(S) MAKE NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, REGARDING THE SOFTWARE. ABSOFT AND ITS LICENSOR(S) DO NOT WARRANT, GUARANTEE OR MAKE ANY REPRESENTATIONS REGARDING THE USE OR THE RESULTS OF THE USE OF THE SOFTWARE IN TERMS OF ITS CORRECTNESS, ACCURACY, RELIABILITY, CURRENTNESS, OR OTHERWISE. THE ENTIRE RISK AS TO THE RESULTS AND PERFORMANCE OF THE SOFTWARE IS ASSUMED BY YOU. THE EXCLUSION OF IMPLIED WARRANTIES IS NOT PERMITTED BY SOME STATES. THE ABOVE EXCLUSION MAY NOT APPLY TO YOU. IN NO EVENT WILL ABSOFT, ITS DIRECTORS, OFFICERS, EMPLOYEES OR LICENSOR(S) BE LIABLE TO YOU FOR ANY CONSEQUENTIAL, INCIDENTAL OR INDIRECT DAMAGES (INCLUDING DAMAGES FOR LOSS OF BUSINESS PROFITS, BUSINESS INTERRUPTION, LOSS OF BUSINESS INFORMATION, AND THE LIKE) ARISING OUT OF THE USE OR INABILITY TO USE THE SOFTWARE EVEN IF ABSOFT HAS BEEN ADVISED OF THE POSSIBILITY OF SUCH DAMAGES. BECAUSE SOME STATES DO NOT ALLOW THE EXCLUSION OR LIMITATION OF LIABILITY FOR CONSEQUENTIAL OR INCIDENTAL DAMAGES, THE ABOVE LIMITATIONS MAY NOT APPLY TO YOU. Absoft and its licensor(s) liability to you for actual damages for any cause whatsoever, and regardless of the form of the action (whether in contract, tort, (including negligence), product liability or otherwise), will be limited to $50. Absoft, the Absoft logo, Fx, Fx2, Pro Fortran, and MacFortran are trademarks of Absoft Corporation Apple, the Apple logo, Velocity Engine, OS 9, and OS X are registered trademarks of Apple Computer, Inc. AMD64 and Opteron are trademarks of AMD Corporation CF90 is a trademark of Cray Research, Inc. IBM, MVS, RS/6000, XL Fortran, and XL C/C++ are trademarks of IBM Corp. Macintosh, NeXT, and NeXTSTEP, are trademarks of Apple Computer, Inc., used under license. MS-DOS is a trademark of Microsoft Corp. Pentium, Pentium Pro, and Pentium II are trademarks of Intel Corp. PowerPC is a trademark of IBM Corp., used under license. Sun and SPARC are trademarks of Sun Microsystems Computer Corp. UNIX is a trademark of the Santa Cruz Operation, Inc. Windows 95/98/NT/ME/2000 and XP are trademarks of Microsoft Corp. All other brand or product names are trademarks of their respective holders. Copyright © 1991-2011 Absoft Corporation and its licensor(s). All Rights Reserved Printed and manufactured in the United States of America. 1.0.1110110 i Fortran Language Reference Contents CHAPTER 1 INTRODUCTION..................................................1 Introduction to This Manual......................................................................................................................1 Introduction to Absoft Fortran..................................................................................................................1 Compatibility...............................................................................................................................................1 Conventions Used in this Manual ..............................................................................................................2 CHAPTER 2 THE FORTRAN PROGRAM .......................3 Character Set...............................................................................................................................................3 Symbolic Names ..........................................................................................................................................4 Keywords .....................................................................................................................................................4 Labels ...........................................................................................................................................................5 Statements....................................................................................................................................................5 Executable Statements..............................................................................................................................5 Nonexecutable Statements........................................................................................................................6 Statement Format......................................................................................................................................6 FORTRAN 77 Fixed Format...............................................................................................................7 Fortran 90 Free Format........................................................................................................................9 VAX FORTRAN Tab-Format...........................................................................................................10 Multiple Statement Lines........................................................................................................................10 Statement Order......................................................................................................................................11 INCLUDE Statement..............................................................................................................................11 Conditional Compilation Statements......................................................................................................12 type and KIND...........................................................................................................................................14 Data Items..................................................................................................................................................14 Constants ................................................................................................................................................15 Character Constant.............................................................................................................................15 Logical Constant................................................................................................................................16 Integer Constant.................................................................................................................................17 Alternate Integer Bases .................................................................................................................17 Real Constant.....................................................................................................................................18 Complex Constant .............................................................................................................................19 Hollerith Constant..............................................................................................................................19 Variables.................................................................................................................................................19 Substrings ...............................................................................................................................................20 Storage........................................................................................................................................................20 Numeric Storage Unit.............................................................................................................................21 Character Storage Unit ...........................................................................................................................21 ii Storage Sequence................................................................................................................................... 21 Storage Association ............................................................................................................................... 21 Storage Definition.................................................................................................................................. 22 CHAPTER 3 SPECIFICATION AND DATA
Recommended publications
  • Fortran 90 Overview
    1 Fortran 90 Overview J.E. Akin, Copyright 1998 This overview of Fortran 90 (F90) features is presented as a series of tables that illustrate the syntax and abilities of F90. Frequently comparisons are made to similar features in the C++ and F77 languages and to the Matlab environment. These tables show that F90 has significant improvements over F77 and matches or exceeds newer software capabilities found in C++ and Matlab for dynamic memory management, user defined data structures, matrix operations, operator definition and overloading, intrinsics for vector and parallel pro- cessors and the basic requirements for object-oriented programming. They are intended to serve as a condensed quick reference guide for programming in F90 and for understanding programs developed by others. List of Tables 1 Comment syntax . 4 2 Intrinsic data types of variables . 4 3 Arithmetic operators . 4 4 Relational operators (arithmetic and logical) . 5 5 Precedence pecking order . 5 6 Colon Operator Syntax and its Applications . 5 7 Mathematical functions . 6 8 Flow Control Statements . 7 9 Basic loop constructs . 7 10 IF Constructs . 8 11 Nested IF Constructs . 8 12 Logical IF-ELSE Constructs . 8 13 Logical IF-ELSE-IF Constructs . 8 14 Case Selection Constructs . 9 15 F90 Optional Logic Block Names . 9 16 GO TO Break-out of Nested Loops . 9 17 Skip a Single Loop Cycle . 10 18 Abort a Single Loop . 10 19 F90 DOs Named for Control . 10 20 Looping While a Condition is True . 11 21 Function definitions . 11 22 Arguments and return values of subprograms . 12 23 Defining and referring to global variables .
    [Show full text]
  • 2021 User Guide
    i Pro Fortran Linux Absoft Pro Fortran User Guide Absoft Fortran Linux Fortran User Guide 5119 Highland Road, PMB 398 Waterford, MI 48327 U.S.A. Tel (248) 220-1190 Fax (248) 220-1194 [email protected] All rights reserved. No part of this publication may be reproduced or used in any form by any means, without the prior written permission of Absoft Corporation. THE INFORMATION CONTAINED IN THIS PUBLICATION IS BELIEVED TO BE ACCURATE AND RELIABLE. HOWEVER, ABSOFT CORPORATION MAKES NO REPRESENTATION OF WARRANTIES WITH RESPECT TO THE PROGRAM MATERIAL DESCRIBED HEREIN AND SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. FURTHER, ABSOFT RESERVES THE RIGHT TO REVISE THE PROGRAM MATERIAL AND MAKE CHANGES THEREIN FROM TIME TO TIME WITHOUT OBLIGATION TO NOTIFY THE PURCHASER OF THE REVISION OR CHANGES. IN NO EVENT SHALL ABSOFT BE LIABLE FOR ANY INCIDENTAL, INDIRECT, SPECIAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE PURCHASER'S USE OF THE PROGRAM MATERIAL. U.S. GOVERNMENT RESTRICTED RIGHTS — The software and documentation are provided with RESTRICTED RIGHTS. Use, duplication, or disclosure by the Government is subject to restrictions set forth in subparagraph (c) (1) (ii) of the Rights in Technical Data and Computer Software clause at 252.227-7013. The contractor is Absoft Corporation, 2111 Cass Lake Rd. Ste 102, Keego Harbor, Michigan 48320. ABSOFT CORPORATION AND ITS LICENSOR(S) MAKE NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, REGARDING THE SOFTWARE. ABSOFT AND ITS LICENSOR(S) DO NOT WARRANT, GUARANTEE OR MAKE ANY REPRESENTATIONS REGARDING THE USE OR THE RESULTS OF THE USE OF THE SOFTWARE IN TERMS OF ITS CORRECTNESS, ACCURACY, RELIABILITY, CURRENTNESS, OR OTHERWISE.
    [Show full text]
  • Quick Overview: Complex Numbers
    Quick Overview: Complex Numbers February 23, 2012 1 Initial Definitions Definition 1 The complex number z is defined as: z = a + bi (1) p where a, b are real numbers and i = −1. Remarks about the definition: • Engineers typically use j instead of i. • Examples of complex numbers: p 5 + 2i; 3 − 2i; 3; −5i • Powers of i: i2 = −1 i3 = −i i4 = 1 i5 = i i6 = −1 i7 = −i . • All real numbers are also complex (by taking b = 0). 2 Visualizing Complex Numbers A complex number is defined by it's two real numbers. If we have z = a + bi, then: Definition 2 The real part of a + bi is a, Re(z) = Re(a + bi) = a The imaginary part of a + bi is b, Im(z) = Im(a + bi) = b 1 Im(z) 4i 3i z = a + bi 2i r b 1i θ Re(z) a −1i Figure 1: Visualizing z = a + bi in the complex plane. Shown are the modulus (or length) r and the argument (or angle) θ. To visualize a complex number, we use the complex plane C, where the horizontal (or x-) axis is for the real part, and the vertical axis is for the imaginary part. That is, a + bi is plotted as the point (a; b). In Figure 1, we can see that it is also possible to represent the point a + bi, or (a; b) in polar form, by computing its modulus (or size), and angle (or argument): p r = jzj = a2 + b2 θ = arg(z) We have to be a bit careful defining φ, since there are many ways to write φ (and we could add multiples of 2π as well).
    [Show full text]
  • Benefits of Continuing Fortran Standardisation Survey: Interim Results
    Benefits of continuing Fortran standardisation survey: interim results Anton Shterenlikht Standards Officer, BCS Fortran Specialist Group 31st August 2018 1 Introduction This survey has been developed by the committee of the BCS Fortran Group to quantify the value of modern Fortran standards to organisations and individuals. We wanted to know how newer Fortran standards have increased the quality of users' code, cut development costs, increased portability or performance, or whether users could attach any monetary value to the benefits enabled by modern Fortran standards. The Fortran language has been steadily developing since its origins in 1957. Many people have been working on revising the Fortran specification, resulting in Fortran 77, 90, 95, 2003, 2008 and 2018 standards. This survey is designed to find out exactly what benefits newer Fortran standards bring to the community. The results of the survey will help the Group justify continuing involvement in Fortran standardisation efforts. The results of the survey will also be shared with the ISO Fortran standardisation committee. The survey is still open at: https://goo.gl/forms/JUFUReOoVUin2m8D2 and will close on 31-DEC-2018. This interim report contains the data received by 31-AUG-2018. All questions were optional, hence the number of responses is given for each question. The percentages for each question are calculated based on the number of responses for that particular question. For fields where the respondents could enter any text, the responses are given verbatim, one response per paragraph. Multiple identical responses in such fields are indicated with numbers in brackets after such responses. We apologise for broken formatting in the longer responses.
    [Show full text]
  • Fortran Resources 1
    Fortran Resources 1 Ian D Chivers Jane Sleightholme May 7, 2021 1The original basis for this document was Mike Metcalf’s Fortran Information File. The next input came from people on comp-fortran-90. Details of how to subscribe or browse this list can be found in this document. If you have any corrections, additions, suggestions etc to make please contact us and we will endeavor to include your comments in later versions. Thanks to all the people who have contributed. Revision history The most recent version can be found at https://www.fortranplus.co.uk/fortran-information/ and the files section of the comp-fortran-90 list. https://www.jiscmail.ac.uk/cgi-bin/webadmin?A0=comp-fortran-90 • May 2021. Major update to the Intel entry. Also changes to the editors and IDE section, the graphics section, and the parallel programming section. • October 2020. Added an entry for Nvidia to the compiler section. Nvidia has integrated the PGI compiler suite into their NVIDIA HPC SDK product. Nvidia are also contributing to the LLVM Flang project. Updated the ’Additional Compiler Information’ entry in the compiler section. The Polyhedron benchmarks discuss automatic parallelisation. The fortranplus entry covers the diagnostic capability of the Cray, gfortran, Intel, Nag, Oracle and Nvidia compilers. Updated one entry and removed three others from the software tools section. Added ’Fortran Discourse’ to the e-lists section. We have also made changes to the Latex style sheet. • September 2020. Added a computer arithmetic and IEEE formats section. • June 2020. Updated the compiler entry with details of standard conformance.
    [Show full text]
  • Fortran Math Special Functions Library
    IMSL® Fortran Math Special Functions Library Version 2021.0 Copyright 1970-2021 Rogue Wave Software, Inc., a Perforce company. Visual Numerics, IMSL, and PV-WAVE are registered trademarks of Rogue Wave Software, Inc., a Perforce company. IMPORTANT NOTICE: Information contained in this documentation is subject to change without notice. Use of this docu- ment is subject to the terms and conditions of a Rogue Wave Software License Agreement, including, without limitation, the Limited Warranty and Limitation of Liability. ACKNOWLEDGMENTS Use of the Documentation and implementation of any of its processes or techniques are the sole responsibility of the client, and Perforce Soft- ware, Inc., assumes no responsibility and will not be liable for any errors, omissions, damage, or loss that might result from any use or misuse of the Documentation PERFORCE SOFTWARE, INC. MAKES NO REPRESENTATION ABOUT THE SUITABILITY OF THE DOCUMENTATION. THE DOCU- MENTATION IS PROVIDED "AS IS" WITHOUT WARRANTY OF ANY KIND. PERFORCE SOFTWARE, INC. HEREBY DISCLAIMS ALL WARRANTIES AND CONDITIONS WITH REGARD TO THE DOCUMENTATION, WHETHER EXPRESS, IMPLIED, STATUTORY, OR OTHERWISE, INCLUDING WITHOUT LIMITATION ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PAR- TICULAR PURPOSE, OR NONINFRINGEMENT. IN NO EVENT SHALL PERFORCE SOFTWARE, INC. BE LIABLE, WHETHER IN CONTRACT, TORT, OR OTHERWISE, FOR ANY SPECIAL, CONSEQUENTIAL, INDIRECT, PUNITIVE, OR EXEMPLARY DAMAGES IN CONNECTION WITH THE USE OF THE DOCUMENTATION. The Documentation is subject to change at any time without notice. IMSL https://www.imsl.com/ Contents Introduction The IMSL Fortran Numerical Libraries . 1 Getting Started . 2 Finding the Right Routine . 3 Organization of the Documentation . 4 Naming Conventions .
    [Show full text]
  • Absoft Pro Fortran User Guide
    Pro Fortran Windows™ User Guide For 32-bit and 64-bit Windows Pro Fortran Windows™ User Guide For 32-bit and 64-bit Windows 2111 Cass Lake Road, Suite 102 Troy, MI 48084 U.S.A. Tel (248) 220-1190 Fax (248) 220-1194 [email protected] All rights reserved. No part of this publication may be reproduced or used in any form by any means, without the prior written permission of Absoft Corporation. THE INFORMATION CONTAINED IN THIS PUBLICATION IS BELIEVED TO BE ACCURATE AND RELIABLE. HOWEVER, ABSOFT CORPORATION MAKES NO REPRESENTATION OF WARRANTIES WITH RESPECT TO THE PROGRAM MATERIAL DESCRIBED HEREIN AND SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. FURTHER, ABSOFT RESERVES THE RIGHT TO REVISE THE PROGRAM MATERIAL AND MAKE CHANGES THEREIN FROM TIME TO TIME WITHOUT OBLIGATION TO NOTIFY THE PURCHASER OF THE REVISION OR CHANGES. IN NO EVENT SHALL ABSOFT BE LIABLE FOR ANY INCIDENTAL, INDIRECT, SPECIAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE PURCHASER'S USE OF THE PROGRAM MATERIAL. U.S. GOVERNMENT RESTRICTED RIGHTS — The software and documentation are provided with RESTRICTED RIGHTS. Use, duplication, or disclosure by the Government is subject to restrictions set forth in subparagraph (c) (1) (ii) of the Rights in Technical Data and Computer Software clause at 252.227-7013. The contractor is Absoft Corporation, 2111 Cass Lake Rd, Suite 102, Keego Harbr, Michigan 48320. ABSOFT CORPORATION AND ITS LICENSOR(S) MAKE NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, REGARDING THE SOFTWARE.
    [Show full text]
  • Absoft Pro Fortran User Guide
    Pro Fortran Windows™ User Guide For 32-bit and 64-bit Windows Pro Fortran Windows™ User Guide For 32-bit and 64-bit Windows 5119 Highland Rd, PMB 398 Waterford, MI 48327 U.S.A. Tel (248) 220-1190 Fax (248) 220-1194 [email protected] All rights reserved. No part of this publication may be reproduced or used in any form by any means, without the prior written permission of Absoft Corporation. THE INFORMATION CONTAINED IN THIS PUBLICATION IS BELIEVED TO BE ACCURATE AND RELIABLE. HOWEVER, ABSOFT CORPORATION MAKES NO REPRESENTATION OF WARRANTIES WITH RESPECT TO THE PROGRAM MATERIAL DESCRIBED HEREIN AND SPECIFICALLY DISCLAIMS ANY IMPLIED WARRANTIES OF MERCHANTABILITY OR FITNESS FOR ANY PARTICULAR PURPOSE. FURTHER, ABSOFT RESERVES THE RIGHT TO REVISE THE PROGRAM MATERIAL AND MAKE CHANGES THEREIN FROM TIME TO TIME WITHOUT OBLIGATION TO NOTIFY THE PURCHASER OF THE REVISION OR CHANGES. IN NO EVENT SHALL ABSOFT BE LIABLE FOR ANY INCIDENTAL, INDIRECT, SPECIAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE PURCHASER'S USE OF THE PROGRAM MATERIAL. U.S. GOVERNMENT RESTRICTED RIGHTS — The software and documentation are provided with RESTRICTED RIGHTS. Use, duplication, or disclosure by the Government is subject to restrictions set forth in subparagraph (c) (1) (ii) of the Rights in Technical Data and Computer Software clause at 252.227-7013. The contractor is Absoft Corporation, 2111 Cass Lake Rd, Suite 102, Keego Harbor, Michigan 48320. ABSOFT CORPORATION AND ITS LICENSOR(S) MAKE NO WARRANTIES, EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE, REGARDING THE SOFTWARE.
    [Show full text]
  • IEEE Standard 754 for Binary Floating-Point Arithmetic
    Work in Progress: Lecture Notes on the Status of IEEE 754 October 1, 1997 3:36 am Lecture Notes on the Status of IEEE Standard 754 for Binary Floating-Point Arithmetic Prof. W. Kahan Elect. Eng. & Computer Science University of California Berkeley CA 94720-1776 Introduction: Twenty years ago anarchy threatened floating-point arithmetic. Over a dozen commercially significant arithmetics boasted diverse wordsizes, precisions, rounding procedures and over/underflow behaviors, and more were in the works. “Portable” software intended to reconcile that numerical diversity had become unbearably costly to develop. Thirteen years ago, when IEEE 754 became official, major microprocessor manufacturers had already adopted it despite the challenge it posed to implementors. With unprecedented altruism, hardware designers had risen to its challenge in the belief that they would ease and encourage a vast burgeoning of numerical software. They did succeed to a considerable extent. Anyway, rounding anomalies that preoccupied all of us in the 1970s afflict only CRAY X-MPs — J90s now. Now atrophy threatens features of IEEE 754 caught in a vicious circle: Those features lack support in programming languages and compilers, so those features are mishandled and/or practically unusable, so those features are little known and less in demand, and so those features lack support in programming languages and compilers. To help break that circle, those features are discussed in these notes under the following headings: Representable Numbers, Normal and Subnormal, Infinite
    [Show full text]
  • A Practical Introduction to Python Programming
    A Practical Introduction to Python Programming Brian Heinold Department of Mathematics and Computer Science Mount St. Mary’s University ii ©2012 Brian Heinold Licensed under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported Li- cense Contents I Basics1 1 Getting Started 3 1.1 Installing Python..............................................3 1.2 IDLE......................................................3 1.3 A first program...............................................4 1.4 Typing things in...............................................5 1.5 Getting input.................................................6 1.6 Printing....................................................6 1.7 Variables...................................................7 1.8 Exercises...................................................9 2 For loops 11 2.1 Examples................................................... 11 2.2 The loop variable.............................................. 13 2.3 The range function............................................ 13 2.4 A Trickier Example............................................. 14 2.5 Exercises................................................... 15 3 Numbers 19 3.1 Integers and Decimal Numbers.................................... 19 3.2 Math Operators............................................... 19 3.3 Order of operations............................................ 21 3.4 Random numbers............................................. 21 3.5 Math functions............................................... 21 3.6 Getting
    [Show full text]
  • A Fast-Start Method for Computing the Inverse Tangent
    A Fast-Start Method for Computing the Inverse Tangent Peter Markstein Hewlett-Packard Laboratories 1501 Page Mill Road Palo Alto, CA 94062, U.S.A. [email protected] Abstract duction method is handled out-of-loop because its use is rarely required.) In a search for an algorithm to compute atan(x) For short latency, it is often desirable to use many in- which has both low latency and few floating point in- structions. Different sequences may be optimal over var- structions, an interesting variant of familiar trigonom- ious subdomains of the function, and in each subdomain, etry formulas was discovered that allow the start of ar- instruction level parallelism, such as Estrin’s method of gument reduction to commence before any references to polynomial evaluation [3] reduces latency at the cost of tables stored in memory are needed. Low latency makes additional intermediate calculations. the method suitable for a closed subroutine, and few In searching for an inverse tangent algorithm, an un- floating point operations make the method advantageous usual method was discovered that permits a floating for a software-pipelined implementation. point argument reduction computation to begin at the first cycle, without first examining a table of values. While a table is used, the table access is overlapped with 1Introduction most of the argument reduction, helping to contain la- tency. The table is designed to allow a low degree odd Short latency and high throughput are two conflict- polynomial to complete the approximation. A new ap- ing goals in transcendental function evaluation algo- proach to the logarithm routine [1] which motivated this rithm design.
    [Show full text]
  • Appendix a Mathematical Fundamentals
    Appendix A Mathematical Fundamentals In this book, it is assumed that the reader has familiarity with the mathematical definitions from the areas of Linear Algebra, Trigonometry, and other related areas. Some of them that are introduced in this Appendix to make the reader quickly understand the derivations and notations used in different chapters of this book. A.1 Function ‘Atan2’ The usual inverse tangent function denoted by Atan(z), where z=y/x, returns an angle in the range (-π/2, π/2). In order to express the full range of angles it is useful to define the so called two- argument arctangent function denoted by Atan2(y,x), which returns angle in the entire range, i.e., (- π, π). This function is defined for all (x,y)≠0, and equals the unique angle θ such that x y cosθ = , and sinθ = …(A.1) x 2 + y 2 x 2 + y 2 The function uses the signs of x and y to select the appropriate quadrant for the angle θ, as explained in Table A.1. Table A.1 Evaluation of ‘Atan2’ function x Atan2(y,x) +ve Atan(z) 0 Sgn(y) π/2 -ve Atan(z)+ Sgn(y) π In Table A.1, z=y/x, and Sgn(.) denotes the usual sign function, i.e., its value is -1, 0, or 1 depending on the positive, zero, and negative values of y, respectively. However, if both x and y are zeros, ‘Atan2’ is undefined. Now, using the table, Atan2(-1,1)= -π/4 and Atan2(1,-1)= 3π/4, whereas the Atan(-1) returns -π/4 in both the cases.
    [Show full text]