NAG Fortran Library, Mark 20

FLSG620SAL - License Managed

Silicon Graphics (IRIX 6) Single Precision

Users' Note



Contents


1. 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", you should consult this note.

In addition, NAG recommends that before calling any library routine you should read the following reference material (see Section 5):

(a) Essential Introduction
(b) Chapter Introduction
(c) Routine Document

If you intend to use the NAG library within a multithreaded application please refer to the document on Thread Safety.

The libraries supplied with this implementation have been compiled in a manner that facilitates the use of multiple threads.

2. Availability of Routines

The routines listed in the chapter contents documents of the NAG Fortran Library Manual, Mark 20 are available in this implementation, with the exception of the following: G13FAE, G13FBE, G13FCE, G13FDE, G13FEE, G13FFE, G13FGE and G13FHE.

At Mark 20, 95 new primary ("user-callable") routines (including the eight listed above) and 36 thread safe equivalents of existing routines were introduced in the NAG Fortran Library. Two routines were deleted. Please consult Mark 20 News (see Section 5) for lists of these routines and for a list of routines scheduled for withdrawal at Mark 21 or later. Your suggestions for new algorithms for future releases of the Library are welcomed (see Section 7).

3. General Information

3.1. Accessing the Library

This implementation includes libraries for the following combinations of Application Binary Interfaces ABI) and Instruction Set Architectures (ISA):

high performance 32-bit (-n32) mode using -mips3
high performance 32-bit (-n32) mode using -mips4
64-bit mode using -mips3
64-bit mode using -mips4

You may link to the NAG Fortran Library in the following manner: 

f77 driver.f -lnagbl -lpthread
where driver.f is your application program. The ABI and ISA of the library included in the link are determined by the compiler's defaults or use of the options -n32/-64 and/or -mips3/-mips4.

If the SGI Scientific Library (SCSL) is avaliable on your system, you may take advantage of this by using the alternative library libnag.a, e.g.: 

f77 driver.f -lnag -lscs -lpthread
The libraries in this implementation are compatible with SGI MIPSpro Compilers f90, but the routines X04ACE and X04ADE should not be used with f90.

3.2. Example Programs

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 c06eae
will copy the example program and its data into the files c06eaee.f and c06eaee.d in the current directory and process them to produce the example program results.

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 Section 3.3.

In other routine documents, the example programs are in single precision. All printed example programs show routine names ending in F not E (see Section 3.5).

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 the distributed example programs are those used in this implementation and may not correspond exactly with the programs published in the manual. The distributed example programs should be used in preference wherever possible.

The distributed example results are those obtained with the NAG 32-bit MIPS IV library, using the NAG BLAS and LAPACK routines. Running the examples with a different ABI/ISA library or non-NAG BLAS or LAPACK may give slightly different results.

3.3. Interpretation of Bold Italicised Terms

For this single precision implementation, the bold italicised terms used in the NAG Fortran Library Manual should be interpreted as: 
real                 - REAL (REAL*4)
basic precision      - single precision
complex              - COMPLEX (COMPLEX*8)
additional precision - double precision (REAL*8,COMPLEX*16)
machine precision    - the machine precision, see the value
                       returned by X02AJE in Section 4

Thus a parameter described as real should be declared as REAL in your program. If a routine accumulates an inner product in additional precision, it is using double precision.

In routine documents that have been typeset since Mark 12 additional bold italicised terms are used in the published example programs and they must be interpreted as follows: 

real as an intrinsic function name - REAL
imag                               - AIMAG
cmplx                              - CMPLX
conjg                              - CONJG
e in constants, e.g. 1.0e-4        - E, e.g. 1.0E-4
e in formats, e.g. e12.4           - E, e.g. E12.4

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: 

sgetrf refers to the LAPACK routine name - SGETRF
cpotrs                                   - CPOTRS

3.4. 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 Section 4.) The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified. These routines are potentially not thread safe and in general output is not recommended in a multithreaded environment.

3.5. 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, or from A to B. Thus, for example: 
A02AAF  denotes the double precision version
A02AAE  denotes the single precision version

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 almost 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.

Chapters C05, D03 and E04 have some routines whose last letter is A rather than F (B in single precision implementations). An A version is always paired with an F routine, the A version being safe to use in a multithreaded environment, but otherwise having identical functionality to the F version. When using the manual in conjunction with this single precision implementation, all names ending in A must be understood to refer to the single precision versions with names ending in B.

The names of COMMON blocks have also been modified, e.g. AD02BJ is renamed BJD02A. This is unlikely to affect the user.

3.6. Interface Blocks

The NAG Fortran Library Interface Blocks define the type and arguments of each user callable NAG Fortran Library routine. These are not essential to calling the NAG Fortran Library from Fortran 90/95 programs. Their purpose is to allow the Fortran 90/95 compiler to check that NAG Fortran Library routines are called correctly. The interface blocks enable the compiler to check that:

(a) Subroutines are called as such
(b) Functions are declared with the right type
(c) The correct number of arguments are passed
(d) All arguments match in type and structure

These interface blocks have been generated automatically by analysing the source code for the NAG Fortran Library. As a consequence, and because these files have been thoroughly tested, their use is recommended in preference to writing your own declarations.

The NAG Fortran Library Interface Block files are organised by Library chapter. The module names are: 

nag_f77_a_chapter
nag_f77_c_chapter
nag_f77_d_chapter
nag_f77_e_chapter
nag_f77_f_chapter
nag_f77_g_chapter
nag_f77_h_chapter
nag_f77_m_chapter
nag_f77_p_chapter
nag_f77_s_chapter
nag_f77_x_chapter
These are supplied in pre-compiled form (.mod files) and they can be accessed by specifying the -I"pathname" option on each f90/95 invocation, where "pathname" is the path of the directory containing the .mod files.

In order to make use of these modules from existing Fortran 77 code the following changes need to be made:

These changes are illustrated by showing the conversion of the Fortran 77 version of the example program for NAG Fortran Library routine S18DEE. Please note that this is not exactly the same as the example program that is distributed with this implementation. Each change is surrounded by comments boxed with asterisks. 

*     S18DEE Example Program Text
*     Mark 14 Revised.  NAG Copyright 1989.
*******************************************************************
* Add USE statement for relevant chapters                         *
      USE NAG_F77_S_CHAPTER
*                                                                 *
*******************************************************************
*     .. Parameters ..
      INTEGER          NIN, NOUT
      PARAMETER        (NIN=5,NOUT=6)
      INTEGER          N
      PARAMETER        (N=2)
*     .. Local Scalars ..
      COMPLEX          Z
      REAL             FNU
      INTEGER          IFAIL, NZ
      CHARACTER*1      SCALE
*     .. Local Arrays ..
      COMPLEX          CY(N)
*     .. External Subroutines ..
*******************************************************************
* EXTERNAL declarations need to be removed (and type declarations *
*  for functions).                                                *
C      EXTERNAL         S18DEE
*                                                                 *
*******************************************************************
*     .. Executable Statements ..
      WRITE (NOUT,*) 'S18DEE Example Program Results'
*     Skip heading in data file
      READ (NIN,*)
      WRITE (NOUT,*)
      WRITE (NOUT,99999) 'Calling with N =', N
      WRITE (NOUT,*)
      WRITE (NOUT,*)
     +'   FNU            Z        SCALE       CY(1)              CY(2)
     +   NZ IFAIL'
      WRITE (NOUT,*)
   20 READ (NIN,*,END=40) FNU, Z, SCALE
      IFAIL = 0
*
      CALL S18DEE(FNU,Z,N,SCALE,CY,NZ,IFAIL)
*
      WRITE (NOUT,99998) FNU, Z, SCALE, CY(1), CY(2), NZ, IFAIL
      GO TO 20
   40 STOP
*
99999 FORMAT (1X,A,I2)
99998 FORMAT (1X,F7.4,'  (',F7.3,',',F7.3,')   ',A,
     +       2('  (',F7.3,',',F7.3,')'),I4,I4)
      END

4. Routine-specific Information

Any further information which applies to one or more routines in this implementation is listed below, chapter by chapter.

(a) D02

D02SAE

The example program results may exhibit failure with IFAIL=14. Users are recommended to use a double precision implementation.

D02TKE

The example program results may exhibit failure with IFAIL=2. Users are recommended to use a double precision implementation.

D02TVE

The example program results may exhibit failure with IFAIL=4; results should be treated with extreme caution. Users are recommended to use a double precision implementation.

D02TXE

The example program results may exhibit failure with IFAIL=2. Users are recommended to use a double precision implementation.

(b) D03

The example programs for D03RAE and D03RBE take much longer to run than other examples.

(c) D05

D05BDE    D05BEE    D05BYE

These routines may fail to solve many problems using this single precision implementation. The use of a double precision implementation is recommended for these routines.

(d) F06, F07 and F08

When using the libnag.a library, calls to the Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) are resolved by calls to the SGI Scientific Library (SCSL), except for the following : 
       caxpyi   cdotci   cdotui   cgthr    cgthrz            csctr 
       saxpyi   sdoti             sgthr    sgthrz   sroti    ssctr

(e) G02

The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0E-4.

(f) G13

G13FAE    G13FBE    G13FCE    G13FDE    G13FEE    G13FCE    G13FGE    G13FHE

These routines are not included in this implementation. The use of a double precision implementation is recommended if these routines are required.

(g) P01

On hard failure, P01ABE writes the error message to the error message unit specified by X04AAE and then stops.

(h) S07 - S21

The constants referred to in the NAG Fortran Library Manual have the following values in this implementation: 
S07AAE  F(1)   = 1.0E+5
        F(2)   = 1.0E-6

S10AAE  E(1)   = 9.2500
S10ABE  E(1)   = 87.00
S10ACE  E(1)   = 87.00

S13AAE  x(hi)  = 87.33
S13ACE  x(hi)  = 2.0E+6
S13ADE  x(hi)  = 2.0E+6

S14AAE  IFAIL  = 1 if X > 33.0
        IFAIL  = 2 if X < -33.0
        IFAIL  = 3 if abs(X) < 1.18E-38
S14ABE  IFAIL  = 2 if X > 4.08E+36

S15ADE  x(hi)  = 9.34
        x(low) = -4.50
S15AEE  x(hi)  = 5.00

S17ACE  IFAIL  = 1 if X > 2.0E+6
S17ADE  IFAIL  = 1 if X > 2.0E+6
        IFAIL  = 3 if 0.0 < X <= 1.18E-38
S17AEE  IFAIL  = 1 if abs(X) > 2.0E+6
S17AFE  IFAIL  = 1 if abs(X) > 2.0E+6
S17AGE  IFAIL  = 1 if X > 25.38
        IFAIL  = 2 if X < -2.1E+4
S17AHE  IFAIL  = 1 if X > 25.79
        IFAIL  = 2 if X < -2.1E+4
S17AJE  IFAIL  = 1 if X > 25.70
        IFAIL  = 2 if X < -1.8E+4
S17AKE  IFAIL  = 1 if X > 25.79
        IFAIL  = 2 if X < -1.8E+4
S17DCE  IFAIL  = 2 if abs (Z) < 2.32E-35
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 2.89E+3
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 8.38E+6
S17DEE  IFAIL  = 2 if imag (Z) > 79.7
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 2.89E+3
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 8.38E+6
S17DGE  IFAIL  = 3 if abs (Z) > 203.
        IFAIL  = 4 if abs (Z) > 4.12E+4
S17DHE  IFAIL  = 3 if abs (Z) > 203.
        IFAIL  = 4 if abs (Z) > 4.12E+4
S17DLE  IFAIL  = 2 if abs (Z) < 2.32E-35
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 2.89E+3
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 8.38E+6

S18ADE  IFAIL  = 2 if 0.0 < X <= 1.18E-38
S18AEE  IFAIL  = 1 if abs(X) > 89.58
S18AFE  IFAIL  = 1 if abs(X) > 89.58
S18CDE  IFAIL  = 2 if 0.0 < X <= 1.18E-38
S18DCE  IFAIL  = 2 if abs (Z) < 2.32E-35
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 2.89E+3
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 8.38E+6
S18DEE  IFAIL  = 2 if real (Z) > 79.7
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 2.89E+3
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 8.38E+6

S19AAE  IFAIL  = 1 if abs(x) >= 18.7500
S19ABE  IFAIL  = 1 if abs(x) >= 18.7500
S19ACE  IFAIL  = 1 if X > 120.44
S19ADE  IFAIL  = 1 if X > 120.44

S21BCE  IFAIL  = 3 if an argument < 1.034E-25
        IFAIL  = 4 if an argument >= 5.337E+23
S21BDE  IFAIL  = 3 if an argument < 2.275E-13
        IFAIL  = 4 if an argument >= 1.741E+12

(i) X01

The values of the mathematical constants are: 
X01AAE (PI)    = 3.1415926535897932D+00
X01ABE (GAMMA) = 0.5772156649015329D+00

(j) X02

The values of the machine constants are:

The basic parameters of the model 

X02BHE =     2
X02BJE =    24
X02BKE =   -125
X02BLE =   128
X02DJE =  .TRUE.
Derived parameters of the floating-point arithmetic 
X02AJE = Z'33800001' ( 5.96047E-8 )
X02AKE = Z'00800000' ( 1.17550E-38 )
X02ALE = Z'7F7FFFFF' ( 3.40282E+38 )
X02AME = Z'00800006' ( 1.17550E-38 )
X02ANE = Z'01000000' ( 2.35099E-38 )
Parameters of other aspects of the computing environment 
X02AHE = Z'4A000000' ( 2.09715E+6 )
X02BBE = 2147483647
X02BEE = 6
X02DAE = .FALSE.

(k) X04

The default output units for error and advisory messages for those routines which can produce explicit output are both Fortran Unit 6.

(l) X05

The finest granularity of wall-clock time available on this system is one second, so the seventh element of the integer array passed as a parameter to X05AAE will always be returned with the value 0.

5. Documentation

Each supported NAG Fortran Library site is ordinarily provided with a printed copy of the NAG Fortran Library Introductory Guide. Additional documentation is available for purchase; please refer to the NAG websites or contact your local NAG Response Centre for current prices (see Section 6).

A full online version of the NAG Fortran Library Manual is supplied in the form of Portable Document Format (PDF) files, with an HTML index, in the NAGdoc directory. The introductory material is also provided as HTML files in the NAGdoc directory.

A main index file has been provided (NAGdoc/fl/html/mark20.html) which contains a fully linked contents document pointing to all the available PDF (and where available HTML) files. Use your HTML browser to navigate from here.

In addition the following are provided in the doc directory:

6. Support from NAG

(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 contact NAG directly at one of the addresses given in the Appendix. Users subscribing to the support service are encouraged to contact one of the NAG Response Centres (see below).

(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 it helps us deal with your enquiry quickly if you can quote your NAG site reference and NAG product code (in this case FLSG620SAL).

(c) NAG Websites

The NAG websites provide information about implementation availability, descriptions of products, downloadable software, product documentation and technical reports. The NAG websites can be accessed at

http://www.nag.co.uk/, http://www.nag.com/ (in North America) or http://www.nag-j.co.jp/ (in Japan)

(d) NAG Electronic Newsletter

If you would like to be kept up to date with news from NAG then please register to receive our free electronic newsletter, which will alert you to special offers, announcements about new products or product/service enhancements, customer stories and NAG's event diary. You can register via one of our websites, or by contacting us at nagnews@nag.co.uk.

7. User Feedback

Many factors influence the way NAG's products and services evolve and your ideas are invaluable in helping us to ensure that we meet your needs. If you would like to contribute to this process we would be delighted to receive your comments. Please contact your local NAG Response Centre (shown below).

Appendix - Contact Addresses

NAG Ltd
Wilkinson House
Jordan Hill Road
OXFORD  OX2 8DR                         NAG Ltd Response Centre
United Kingdom                          email: support@nag.co.uk

Tel: +44 (0)1865 511245                 Tel: +44 (0)1865 311744
Fax: +44 (0)1865 310139                 Fax: +44 (0)1865 310139

NAG Inc
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Downers Grove
IL 60515-1362                           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 2706

Nihon NAG KK
Hatchobori Frontier Building 2F
4-9-9
Hatchobori
Chuo-ku
Tokyo
104-0032
Japan
email: help@nag-j.co.jp

Tel: +81 (0)3 5542 6311
Fax: +81 (0)3 5542 6312