.TH "Users'_Note" "3NAG" "" "Fortran Library" .SH "Name" nag_fl_un \- NAG Fortran Library, Mark 18, Users' Note .SH "Title" .B " NAG Fortran Library, Mark 18 .B " FLCRE18SE .B " Cray T3E Single Precision .B " Users' Note .SH "Introduction" This document is essential reading for every user of the NAG Fortran Library Implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Fortran Library Manual and Introductory Guide. Wherever those manuals refer to the "Users' Note for your implementation", the user should consult this note. NAG recommends that users read the following minimum reference material before calling any library routine: .in +5 .ti -4 (a) Essential Introduction .ti -4 (b) Chapter Introduction .ti -4 (c) Routine Document .ti -4 (d) Implementation-specific Users' Note .in -5 Items (a), (b) and (c) are included in the NAG Fortran Library Manual; items (a) and (b) are also included in the NAG Fortran Library Introductory Guide; item (d) is this document which is provided in man page form. Items (a) and (d) are also supplied on the distribution medium. Each NAG Fortran Library site is supplied with at least one copy of each of the above. Please ask your NAG Site Contact for further information. .SH "Availability of Routines" All routines listed in the chapter contents documents of the NAG Fortran Library Manual, Mark 18 are available in this implementation. At Mark 18, 35 new primary ('user-callable') routines have been introduced, and 76 deleted. Please consult the document FORTRAN MARK 18 NEWS in the manual for lists of these routines and for a list of routines scheduled for withdrawal at Mark 19 or later. The file doc/news supplied to your site on the library distribution medium (see the section "User Documentation" below) also gives an outline of the new material available. .SH "General Information" .SS "Accessing the Library" Assuming that libnag.a has been installed in /usr/local/lib or /usr/lib, then a user may link to the NAG Fortran Library in the following manner: f90 driver.f -lnag where driver.f is the user's application program. .SS "Interpretation of Bold Italicised Terms" For this single precision implementation, the bold italicised terms used in the NAG Fortran Library Manual (and shown here as //.....// ) should be interpreted as: .nf //real// - REAL (REAL*8) //basic precision// - single precision //complex// - COMPLEX*16 //additional precision// - double precision (REAL*16) //machine precision// - the machine precision, see the value returned by X02AJE in the section "Routine-specific Information" below .fi Thus a parameter described as //real// should be declared as REAL in the user's program. If a routine accumulates an inner product in //additional precision//, it is using double precision. In routine documents that have been newly typeset since Mark 12 additional bold italicised terms are used in the published example programs and they must be interpreted as follows: .nf //real// as an intrinsic function name - REAL //imag// - AIMAG //cmplx// - CMPLX //conjg// - CONJG //e// in constants, e.g. 1.0//e//-4 - E, e.g. 1.0E-4 //e// in formats, e.g. //e//12.4 - E, e.g. E12.4 .fi All references to routines in Chapter F07 - Linear Equations (LAPACK) and Chapter F08 - Least-squares and Eigenvalue Problems (LAPACK) use the LAPACK name, not the NAG F07/F08 name. The LAPACK name is precision dependent, and hence the name appears in a bold italicised typeface. For example: .nf //sgetrf// refers to the LAPACK routine name - SGETRF //cpotrs// - CPOTRS .fi .SS "Example Programs" In the NAG Fortran Library Manual, routine documents that have been typeset since Mark 12 present the example programs in a generalised form, using bold italicised terms as described in the section "Interpretation of Bold Italicised Terms" above. In other routine documents, the example programs are in single precision. All printed example programs show routine names ending in F not E, see the section "Naming of Routines" below. The example programs supplied to a site in machine-readable form have been modified as necessary so that they are suitable for immediate execution. Note that all the distributed example programs have been revised and do not correspond exactly with the programs published in the manual, unless the documents have been recently typeset. The distributed example programs should be used in preference wherever possible. The example programs are most easily accessed by the command nagexample, which will provide you with a copy of an example program (and its data, if any), compile the program and link it with the library (showing you the compile command so that you can recompile your own version of the program). Finally, the executable program will be run, presenting its output to stdout. The example program concerned is specified by the argument to nagexample, e.g. nagexample c02afe will copy the example program and its data into the files c02afee.f and c02afee.d in the current directory and process them to produce the example program results. Further usage details may be obtained by using the command nagexample without arguments. .SS "Explicit Output from NAG Routines" Certain routines produce explicit error messages and advisory messages via output units which either have default values or can be reset by using X04AAE for error messages and X04ABE for advisory messages. (The default values are given in the section "Routine-specific Information" below). The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified. .SS "User Documentation" The following information is provided in man page form: nag_fl_un.3 - Users' Note (this document) The following machine-readable information files are provided by NAG on the library distribution medium. Please consult your local advisory service or NAG Site Contact for further details: .nf essint - the Essential Introduction to the NAG Fortran Library summary - a brief summary of the routines news - an outline of the new and enhanced routines available at Mark 18 replaced - a list of routines available at earlier Marks of the Library but since withdrawn, together with recommended replacements calls - a list of routines called directly or indirectly by each routine in the library, and by each example program called - for each routine in the library (including auxiliaries), a list of routines and example programs which call it directly or indirectly .fi See the section "Additional Services from NAG" below for additional documentation available from NAG. .SS "Naming of Routines To ensure a single precision implementation is completely distinct from any double precision version also available, all single precision routine names have been modified by changing the sixth character from F to E. Thus, for example: .nf A02AAF denotes the double precision version A02AAE denotes the single precision version .fi The names of auxiliary routines have also been modified by interchanging the first three and the last three characters, e.g. C02AFZ has been changed to AFZC02. In the NAG Fortran Library Manual all library routine names end in F. Therefore, when using the manual in conjunction with this single precision implementation, all such names must be understood to refer to the single precision versions with names ending in E. Some routines in the Library require users to specify particular auxiliary routines. Again, when using this implementation it is necessary to specify the amended names, as given in the section "Routine-specific Information" below. The names of COMMON blocks have also been modified, e.g. AC02AF is renamed AFC02A. This is unlikely to affect the user. .SH "Routine-specific Information" Any further information which applies to one or more routines in this implementation is listed below, chapter by chapter. .ti -4 (a) D01 .nf D01BAE Auxiliaries D01BAW, D01BAX, D01BAY and D01BAZ have been renamed as BAWD01, BAXD01, BAYD01 and BAZD01 respectively. D01BBE Auxiliaries D01BAW, D01BAX, D01BAY and D01BAZ have been renamed as BAWD01, BAXD01, BAYD01 and BAZD01 respectively. D01FDE Auxiliary D01FDV has been renamed as FDVD01. .fi .ti -4 (b) D02 .nf D02BJE Auxiliaries D02BJW and D02BJX have been renamed as BJWD02 and BJXD02 respectively. D02EJE Auxiliaries D02EJW, D02EJX and D02EJY have been renamed as EJWD02, EJXD02 and EJYD02 respectively. D02NBE Auxiliaries D02NBY and D02NBZ have been renamed as NBYD02 and NBZD02 respectively. D02NCE Auxiliaries D02NBY and D02NCZ have been renamed as NBYD02 and NCZD02 respectively. D02NDE Auxiliaries D02NBY and D02NDZ have been renamed as NBYD02 and NDZD02 respectively. D02NGE Auxiliaries D02NBY and D02NGZ have been renamed as NBYD02 and NGZD02 respectively. D02NHE Auxiliaries D02NBY and D02NHZ have been renamed as NBYD02 and NHZD02 respectively. D02NJE Auxiliaries D02NBY and D02NJZ have been renamed as NBYD02 and NJZD02 respectively. D02RAE Auxiliaries D02GAX and D02GAZ have been renamed as GAXD02 and GAZD02 respectively. D02SAE Auxiliaries D02HBW, D02HBX, D02HBY and D02HBZ have been renamed as HBWD02, HBXD02, HBYD02 and HBZD02 respectively. .fi .ti -4 (c) D03 The example programs for D03RAE and D03RBE take much longer to run than other examples: D03RAE takes about seven minutes and D03RBE about twenty minutes to run on a Silicon Graphics Iris Indigo in double precision. .nf D03PFE Auxiliary D03PFP has been renamed as PFPD03. D03PHE Auxiliary D03PCK has been renamed as PCKD03. D03PJE Auxiliary D03PCK has been renamed as PCKD03. D03PKE Auxiliary D03PEK has been renamed as PEKD03. D03PLE Auxiliaries D03PEK and D03PLP have been renamed as PEKD03 and PLPD03 respectively. D03PPE Auxiliaries D03PCK and D03PCL have been renamed as PCKD03 and PCLD03 respectively. D03PRE Auxiliaries D03PEK and D03PEL have been renamed as PEKD03 and PELD03 respectively. D03PSE Auxiliaries D03PEK, D03PEL and D03PLP have been renamed as PEKD03, PELD03 and PLPD03 respectively. D03PWE Auxiliaries D03PEK and D03PLP have been renamed as PEKD03 and PLPD03 respectively. D03PXE Auxiliaries D03PEK and D03PLP have been renamed as PEKD03 and PLPD03 respectively. .fi .ti -4 (d) E04 .nf E04GBE Auxiliaries E04FCV and E04HEV have been renamed as FCVE04 and HEVE04 respectively. E04NFE Auxiliary E04NFU has been renamed as NFUE04. E04NKE Auxiliary E04NKU has been renamed as NKUE04. E04UCE Auxiliary E04UDM has been renamed as UDME04. E04UNE Auxiliary E04UDM has been renamed as UDME04. E04UPE Auxiliary E04UDM has been renamed as UDME04. E04ZCE Auxiliary E04VDM has been renamed as VDME04. .fi .ti -4 (e) F02 .nf F02FJE Auxiliary F02FJZ has been renamed as FJZF02. .fi .ti -4 (f) F06, F07 and F08 In this implementation calls to the Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) are implemented by calls to the Cray Research libsci.a subroutine library. All calls to BLAS and LAPACK routines use the code in libsci.a except the following, which use NAG versions: .nf SGETRI CGETRI SSTEIN CSTEIN SGEBAK CGEBAK .fi .ti -4 (g) G02 The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0E-13. .ti -4 (h) P01 On hard failure, P01ABE writes the error message to the error message unit specified by X04AAE and then stops. .ti -4 (i) S07 - S21 The constants referred to in the NAG Fortran Library Manual have the following values in this implementation: .nf .in +4 S07AAE F(1) = 1.0E+13 F(2) = 1.0E-14 S10AAE E(1) = 18.50 S10ABE E(1) = 708.0 S10ACE E(1) = 708.0 S13AAE x(hi) = 708.3 S13ACE x(hi) = 3.3E+7 S13ADE x(hi) = 3.3E+7 S14AAE IFAIL = 1 if X > 170.0 IFAIL = 2 if X < -170.0 IFAIL = 3 if abs(X) < 2.23E-308 S14ABE IFAIL = 2 if X > 2.55E+305 S15ADE x(hi) = 26.6 x(low) = -6.25 S15AEE x(hi) = 6.25 S17ACE IFAIL = 1 if X > 3.3E+7 S17ADE IFAIL = 1 if X > 3.3E+7 IFAIL = 3 if 0.0 < X <= 2.23E-308 S17AEE IFAIL = 1 if abs(X) > 3.3E+7 S17AFE IFAIL = 1 if abs(X) > 3.3E+7 S17AGE IFAIL = 1 if X > 103.8 IFAIL = 2 if X < -1.3E+5 S17AHE IFAIL = 1 if X > 104.1 IFAIL = 2 if X < -1.3E+5 S17AJE IFAIL = 1 if X > 104.1 IFAIL = 2 if X < -1.3E+5 S17AKE IFAIL = 1 if X > 104.1 IFAIL = 2 if X < -1.3E+5 S17DCE IFAIL = 2 if abs (Z) < 5.97E-154 IFAIL = 4 if abs (Z) or FNU+N-1 > 6.71E+7 IFAIL = 5 if abs (Z) or FNU+N-1 > 4.50E+15 S17DEE IFAIL = 2 if imag (Z) > 700.0 IFAIL = 3 if abs (Z) or FNU+N-1 > 6.71E+7 IFAIL = 4 if abs (Z) or FNU+N-1 > 4.50E+15 S17DGE IFAIL = 3 if abs (Z) > 1.65E+5 IFAIL = 4 if abs (Z) > 2.72E+10 S17DHE IFAIL = 3 if abs (Z) > 1.65E+5 IFAIL = 4 if abs (Z) > 2.72E+10 S17DLE IFAIL = 2 if abs (Z) < 5.97E-154 IFAIL = 4 if abs (Z) or FNU+N-1 > 6.71E+7 IFAIL = 5 if abs (Z) or FNU+N-1 > 4.50E+15 S18ADE IFAIL = 2 if 0.0 < X <= 2.23E-308 S18AEE IFAIL = 1 if abs(X) > 711.6 S18AFE IFAIL = 1 if abs(X) > 711.6 S18CDE IFAIL = 2 if 0.0 < X <= 2.23E-308 S18DCE IFAIL = 2 if abs (Z) < 5.97E-154 IFAIL = 4 if abs (Z) or FNU+N-1 > 6.71E+7 IFAIL = 5 if abs (Z) or FNU+N-1 > 4.50E+15 S18DEE IFAIL = 2 if real (Z) > 700.0 IFAIL = 3 if abs (Z) or FNU+N-1 > 6.71E+7 IFAIL = 4 if abs (Z) or FNU+N-1 > 4.50E+15 S19AAE IFAIL = 1 if abs(x) >= 49.50 S19ABE IFAIL = 1 if abs(x) >= 49.50 S19ACE IFAIL = 1 if X > 997.26 S19ADE IFAIL = 1 if X > 997.26 S21BCE IFAIL = 3 if an argument < 1.579E-205 IFAIL = 4 if an argument >= 3.774E+202 S21BDE IFAIL = 3 if an argument < 2.820E-103 IFAIL = 4 if an argument >= 1.404E+102 .in -4 .fi .ti -4 (j) X01 The values of the mathematical constants are: .nf .in +4 X01AAE (PI) = 3.1415926535897932 X01ABE (GAMMA) = 0.5772156649015329 .in -4 .fi .ti -4 (k) X02 The values of the machine constants are: The basic parameters of the model .nf .in +4 X02BHE = 2 X02BJE = 53 X02BKE = -1021 X02BLE = 1024 X02DJE = .TRUE. .ti -4 Derived parameters of floating-point arithmetic X02AJE = Z'3CA0000000000001' ( 1.11022302462516E-16 ) X02AKE = Z'0010000000000000' ( 2.22507385850720E-308 ) X02ALE = Z'7FEFFFFFFFFFFFFF' ( 1.79769313486232E+308 ) X02AME = Z'0010000000000000' ( 2.22507385850720E-308 ) X02ANE = Z'2010000000000043' ( 2.98333629248013E-154 ) .ti -4 Parameters of other aspects of the computing environment X02AHE = Z'4180000000000000' ( 3.35544320000000E+7 ) X02BBE = 9223372036854775807 X02BEE = 15 X02DAE = .FALSE. .in -4 .fi .ti -4 (l) X04 The default output units for error and advisory messages for those routines which can produce explicit output are Fortran Units 0 and 6, respectively. .SH "Additional Services from NAG" .ti -4 (a) Documentation Each NAG Fortran Library site is provided with a printed copy of the NAG Fortran Library Manual. Additional manuals are available at prices published in the NAG documentation order form. NAG Fortran Library TextWare, a hypertext version of the full manual, is bundled with this implementation. For a list of supported platforms, see the Installers' Note for the TextWare product. .ti -4 (b) On-line Information Supplement The NAG On-line Information Supplement provides a system to assist with routine selection and gives abbreviated on-line documentation of the routines. It is available in a generic UNIX version. .SH "Support from NAG" .ti -4 (a) Contact with NAG Queries concerning this document or the implementation generally should be directed initially to your local Advisory Service. If you have difficulty in making contact locally, you can write to NAG directly, at one of the supplied addresses. Users subscribing to the support service are encouraged to contact one of the NAG Response Centres (see below). .ti -4 (b) NAG Response Centres The NAG Response Centres are available for general enquiries from all users and also for technical queries from sites with an annually licensed product or support service. The Response Centres are open during office hours, but contact is possible by fax, email and phone (answering machine) at all times. When contacting a Response Centre please quote your NAG user reference and NAG product code. .ti -4 (c) Network Network, NAG's newsletter, is produced periodically and sent free of charge to sites with a supported product or service. .ti -4 (d) NAG Website The NAG Website is an information service providing items of interest to users and prospective users of NAG products and services. The information is regularly updated and reviewed and includes implementation availability, descriptions of products, downloadable software and technical reports. The NAG Website can be accessed at .nf http://www.nag.co.uk/ or http://www.nag.com/ (in the USA) .fi .SH "NAG Users Association" NAGUA, the NAG Users Association, is a self-financing, non-profitmaking body. It exists to promote communications between NAG and users of its products and services. It provides information to NAG on the requirements of users, who are in turn kept informed of developments in services. Membership is available to any institution or individual holding a licence for any NAG product or service. Members receive discounts on the registration fees at conferences and workshops. For an information pack and membership application form, please contact NAGUA at the supplied address. .SH "Appendix - supplied addresses" .nf NAG Ltd Wilkinson House Jordan Hill Road OXFORD OX2 8DR NAG Ltd Response Centre United Kingdom email: infodesk@nag.co.uk Tel: +44 1865 511245 Tel: +44 1865 311744 Fax: +44 1865 310139 Fax: +44 1865 311755 NAG Inc 1400 Opus Place, Suite 200 Downers Grove IL 60515-5702 NAG Inc Response Center USA email: infodesk@nag.com Tel: +1 630 971 2337 Tel: +1 630 971 2345 Fax: +1 630 971 2706 Fax: +1 630 971 2346 NAG GmbH Schleissheimerstrasse 5 D-85748 Garching Deutschland email: naggmbh@nag.co.uk Tel: +49 89 3207395 Fax: +49 89 3207396 NAG Users Association PO Box 426 OXFORD OX2 8SD United Kingdom email: nagua@nag.co.uk Tel: +44 1865 311102