FSL6A21DPL Users' Note

NAG SMP Library, Mark 21

FSL6A21DPL - License Managed

AMD64, Linux 64, PGI Fortran, Double Precision

Users' Note

1. Introduction
2. Availability of Routines
3. General Information
4. Routine-specific Information
5. Documentation
6. Support from NAG
7. User Feedback
Appendix - Contact Addresses

1. Introduction

This document is essential reading for every user of the NAG SMP Library implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Mark 21 Library Manual (which we will refer to as the Library Manual). Wherever that manual refers 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

The libraries supplied with this implementation have not been compiled in a manner that facilitates their use within a multithreaded application.

2. Availability of Routines

All routines listed in the chapter contents documents of the Library Manual are available in this implementation. Please consult Mark 21 News (see Section 5) for a list of new routines and for a list of routines scheduled for withdrawal at future Marks. 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 section shows two ways of accessing the library depending on the location of the compiled libraries.

3.1.1. Libraries NOT in the linker search path

In this section we assume that the library has been installed in the directory [INSTALL_DIR].

By default [INSTALL_DIR] (see Installer's Note (in.html)) is /opt/NAG/fsl6a21dpl or /usr/local/NAG/fsl6a21dpl depending on your system; however it could have been changed by the installer. To identify [INSTALL_DIR] for this installation:

if /opt/NAG/fsl6a21dpl exists, then this is [INSTALL_DIR]
if /usr/local/NAG/fsl6a21dpl exists, then this is [INSTALL_DIR]
consult the installer for the directory [INSTALL_DIR].

To use the NAG SMP and the supplied ACML libraries, you may link in the following manner:

  pgf90 -mp driver.f [INSTALL_DIR]/lib/libnagsmp.a [INSTALL_DIR]/acml3.0.0/lib/libacml.a

where driver.f is your application program; or

  pgf90 -mp driver.f [INSTALL_DIR]/lib/libnagsmp.so [INSTALL_DIR]/acml3.0.0/lib/libacml.so

if the shareable library is required.

If your application has been linked with the shareable NAG and ACML libraries then the environment variable LD_LIBRARY_PATH must be set or extended to allow run time linkage.

In the C shell type:

   setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib

to set LD_LIBRARY_PATH, or

   setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib:${LD_LIBRARY_PATH}

to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

   LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib
   export LD_LIBRARY_PATH

to set LD_LIBRARY_PATH, or

   LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib:${LD_LIBRARY_PATH}
   export LD_LIBRARY_PATH

to extend LD_LIBRARY_PATH if you already have it set.

Note that you may also need to set LD_LIBRARY_PATH to point at other things such as compiler run-time libraries. For example, if you are using a newer version of the PGI compiler than the one used to build the NAG libraries, adding the PGI run-time library directory may be useful, e.g. (Bourne shell):

LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0:/usr/pgi/linux86-64/6.1/libso
   export LD_LIBRARY_PATH

3.1.2. Libraries in the linker search path

In this section we assume that the NAG SMP and the supplied ACML libraries are installed in, or are pointed at by symbolic links from, directories in the search path of the linker, such as /usr/lib.

To use the NAG SMP and the supplied ACML libraries, you may link in the following manner:

  pgf90 -mp driver.f -lnagsmp -lacml

This will usually link to the shareable library in preference to the static library if both the libraries are at the same location.

To use the static library libnagsmp.a you need the -Bstatic compiler flag:

  pgf90 -mp -Bstatic driver.f -lnagsmp -lacml

please note that on some systems you may need to add -Bdynamic at the end of the above statment to allow accessing other libraries that may be avilable only in sharead form.

If your application has been linked with the shareable NAG and ACML libraries then the environment variable LD_LIBRARY_PATH must be set or extended to allow run time linkage.

In the C shell type:

   setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib

to set LD_LIBRARY_PATH, or

   setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib:${LD_LIBRARY_PATH}

to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:

   LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib
   export LD_LIBRARY_PATH

to set LD_LIBRARY_PATH, or

   LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0/lib:${LD_LIBRARY_PATH}
   export LD_LIBRARY_PATH

to extend LD_LIBRARY_PATH if you already have it set.

LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/acml3.0.0:/usr/pgi/linux86-64/6.1/libso
   export LD_LIBRARY_PATH

3.1.3. Set the number of processors to use

Set the environment variable OMP_NUM_THREADS to the number of processors required, up to maximum available on your system, e.g. In the C shell type:

setenv OMP_NUM_THREADS N

In the Bourne shell, type:

set OMP_NUM_THREADS=N
export OMP_NUM_THREADS

where N is the number of processors required. OMP_NUM_THREADS may be re-set between each execution of the program, as desired.

3.2. Example Programs

The directory [INSTALL_DIR]/scripts contains two scripts nagsmp_example and nagsmp_example_shar.

The example programs are most easily accessed by one of the commands

nagsmp_example, to link with the NAG static library libnagsmp.a and the supplied ACML libraries
nagsmp_example_shar, to link with the NAG shareable library libnagsmp.so and the supplied ACML libraries

Each command will provide you with a copy of an example program (and its data, if any), compile the program and link it with the appropriate libraries (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, and the number of OpenMP threads to use, are specified by the arguments to the command, e.g.

nagsmp_example e04ucf 4

will copy the example program and its data into the files e04ucfe.f and e04ucfe.d in the current folder and process them to produce the example program results in the file e04ucfe.r.

The example programs are supplied in machine-readable form. They are suitable for immediate usage. Note that the distributed example programs are those used in this implementation and may not correspond exactly with the programs published in the Library Manual. The distributed example programs should be used in preference wherever possible.

3.3. Interpretation of Bold Italicised Terms

For this double precision implementation, the bold italicised terms used in the Library Manual should be interpreted as follows:

real or double precision  - DOUBLE PRECISION (REAL*8)
basic precision           - double precision
complex or complex*16     - COMPLEX*16
additional precision      - quadruple precision (REAL*16,COMPLEX*32)
machine precision         - the machine precision, see the value
                            returned by X02AJF in Section 4

Thus a parameter described as real or double precision should be declared as DOUBLE PRECISION in your program. If a routine accumulates an inner product in additional precision, it is using software to simulate quadruple precision.

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.

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 X04AAF for error messages and X04ABF 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.

3.5. Interface Blocks

The NAG SMP Library Interface Blocks define the type and arguments of each user callable NAG SMP Library routine. These are not essential to calling the NAG SMP Library from Fortran 90/95 programs. Their purpose is to allow the Fortran 90/95 compiler to check that NAG SMP 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 SMP 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 SMP 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 -Ipathname option on each f90/95 invocation, where pathname ([INSTALL_DIR]/nag_interface_blocks) is the path of the directory containing the compiled interface blocks.

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

Add a USE statement for each of the module files for the chapters of the NAG SMP Library that your program calls directly. Only one USE statement will be required. The interface blocks for the BLAS and LAPACK routines are in nag_f77_f_chapter.
Delete all EXTERNAL statements for NAG SMP Library routines (including BLAS and LAPACK routines). These are now declared in the module(s).
Delete the type declarations for any NAG SMP Library functions. These are now declared in the module(s).

The above steps need to be done for each unit (main program, function or subroutine) in your code.

These changes are illustrated by showing the conversion of the Fortran 77 version of the example program for NAG SMP Library routine D01DAF. 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.

*     D01DAF Example Program Text
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_D_CHAPTER
*                                                   *
*****************************************************
*     .. Parameters ..
      INTEGER          NOUT
      PARAMETER        (NOUT=6)
*     .. Local Scalars ..
      DOUBLE PRECISION ABSACC, ANS, YA, YB
      INTEGER          IFAIL, NPTS
*     .. External Functions ..
      DOUBLE PRECISION FA, FB, P1, P2A, P2B
      EXTERNAL         FA, FB, P1, P2A, P2B
*     .. External Subroutines ..
******************************************************
* EXTERNAL declarations need to be removed.          *
C     EXTERNAL         D01DAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      WRITE (NOUT,*) 'D01DAF Example Program Results'
      YA = 0.0D0
      YB = 1.0D0
      ABSACC = 1.0D-6
      WRITE (NOUT,*)
      WRITE (NOUT,*) 'First formulation'
      IFAIL = 1
*
      CALL D01DAF(YA,YB,P1,P2A,FA,ABSACC,ANS,NPTS,IFAIL)
*
      WRITE (NOUT,99999) 'Integral =', ANS
      WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
      IF (IFAIL.GT.0) WRITE (NOUT,99997) 'IFAIL = ', IFAIL
      WRITE (NOUT,*)
      WRITE (NOUT,*) 'Second formulation'
      IFAIL = 1
*
      CALL D01DAF(YA,YB,P1,P2B,FB,ABSACC,ANS,NPTS,IFAIL)
*
      WRITE (NOUT,99999) 'Integral =', ANS
      WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
      IF (IFAIL.GT.0) WRITE (NOUT,99997) 'IFAIL = ', IFAIL
      STOP
*
99999 FORMAT (1X,A,F9.4)
99998 FORMAT (1X,A,I5)
99997 FORMAT (1X,A,I2)
      END
*
      DOUBLE PRECISION FUNCTION P1(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION             Y
*     .. Executable Statements ..
      P1 = 0.0D0
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION P2A(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION              Y
*     .. Intrinsic Functions ..
      INTRINSIC                     SQRT
*     .. Executable Statements ..
      P2A = SQRT(1.0D0-Y*Y)
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION FA(X,Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION             X, Y
*     .. Executable Statements ..
      FA = X + Y
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION P2B(Y)
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_X_CHAPTER
*                                                   *
*****************************************************
*     .. Scalar Arguments ..
      DOUBLE PRECISION              Y
*     .. External Functions ..
******************************************************
* Function Type declarations need to be removed.     *
C     DOUBLE PRECISION              X01AAF
*                                                    *
******************************************************
******************************************************
* EXTERNAL declarations need to be removed.          *
C     EXTERNAL                      X01AAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      P2B = 0.5D0*X01AAF(0.0D0)
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION FB(X,Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION             X, Y
*     .. Intrinsic Functions ..
      INTRINSIC                    COS, SIN
*     .. Executable Statements ..
      FB = Y*Y*(COS(X)+SIN(X))
      RETURN
      END

4. Routine-specific Information

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

F06, F07 and F08

Many LAPACK routines have a "workspace query" mechanism which allows a caller to interrogate the routine to determine how much workspace to supply. Note that LAPACK routines from the AMD ACML library may require a different amount of workspace than the equivalent NAG versions of these routines. Care should be taken when using the workspace query mechanism.

In this implementation calls to BLAS and LAPACK routines are implemented by calls to AMD ACML , except for the following routines:

DBDSDC    DGBRFS    DGBSV     DGBSVX    DGBTRF    DGBTRS    DGEBRD    DGEES
DGEESX    DGEEV     DGEEVX    DGELS     DGELSD    DGELSS    DGELSY    DGEQP3
DGERFS    DGESDD    DGESV     DGESVD    DGESVX    DGGES     DGGESX    DGGEV
DGGEVX    DGGGLM    DGGLSE    DGGQRF    DGGRQF    DGTRFS    DGTSVX    DHSEIN
DHSEQR    DLALSD    DLASDA    DLASDQ    DOPGTR    DORGBR    DORGHR    DORGQR
DORGTR    DORMBR    DORMHR    DORMQR    DORMTR    DPBRFS    DPBSV     DPBSVX
DPBTRS    DPORFS    DPOSV     DPOSVX    DPPRFS    DPPSV     DPPSVX    DPPTRS
DPTEQR    DPTRFS    DPTSVX    DSBEV     DSBEVD    DSBEVX    DSBGV     DSBGVD
DSBGVX    DSBTRD    DSPEV     DSPEVD    DSPEVX    DSPGV     DSPGVD    DSPGVX
DSPRFS    DSPSVX    DSTEBZ    DSTEDC    DSTEGR    DSTEIN    DSTEV     DSTEVD
DSTEVR    DSTEVX    DSYEV     DSYEVD    DSYEVR    DSYEVX    DSYGV     DSYGVD
DSYGVX    DSYRFS    DSYSVX    DSYTRD    DTBRFS    DTBTRS    DTPRFS    DTPTRS
DTRRFS    ZGBRFS    ZGBSV     ZGBSVX    ZGBTRF    ZGBTRS    ZGEBRD    ZGEES
ZGEESX    ZGEEV     ZGEEVX    ZGELS     ZGELSD    ZGELSS    ZGELSY    ZGEQP3
ZGERFS    ZGESDD    ZGESV     ZGESVD    ZGESVX    ZGGES     ZGGESX    ZGGEV
ZGGEVX    ZGGGLM    ZGGLSE    ZGGQRF    ZGGRQF    ZGTRFS    ZGTSVX    ZHBEV
ZHBEVD    ZHBEVX    ZHBGV     ZHBGVD    ZHBGVX    ZHBTRD    ZHEEV     ZHEEVD
ZHEEVR    ZHEEVX    ZHEGV     ZHEGVD    ZHEGVX    ZHERFS    ZHESVX    ZHETRD
ZHPEV     ZHPEVD    ZHPEVX    ZHPGV     ZHPGVD    ZHPGVX    ZHPRFS    ZHPSVX
ZHSEIN    ZHSEQR    ZLALSD    ZPBRFS    ZPBSV     ZPBSVX    ZPBTRS    ZPORFS
ZPOSV     ZPOSVX    ZPPRFS    ZPPSV     ZPPSVX    ZPPTRS    ZPTEQR    ZPTRFS
ZPTSVX    ZSPRFS    ZSPSVX    ZSTEDC    ZSTEGR    ZSTEIN    ZSYRFS    ZSYSVX
ZTBRFS    ZTBTRS    ZTPRFS    ZTPTRS    ZTRRFS    ZUNGBR    ZUNGHR    ZUNMBR
ZUNMHR    ZUNMQR    ZUNMTR    ZUPGTR

The following NAG named routines are wrappers to call LAPACK routines from the vendor library:

F07ADF    F07AEF    F07ARF    F07ASF    F07FDF    F07FEF    F07FRF    F07FSF
F08AEF    F08ASF    F08ATF    F08FTF    F08JEF    F08JSF    F08MEF    F08MSF

G02

The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0D-13.

P01

On hard failure, P01ABF writes the error message to the error message unit specified by X04AAF and then stops.

S07 - S21

The constants referred to in the NAG Fortran Library Manual have the following values in this implementation:

S07AAF  F(1)   = 1.0D+13
        F(2)   = 1.0D-14

S10AAF  E(1)   = 1.8500D+1
S10ABF  E(1)   = 7.080D+2
S10ACF  E(1)   = 7.080D+2

S13AAF  x(hi)  = 7.083D+2
S13ACF  x(hi)  = 1.0D+16
S13ADF  x(hi)  = 1.0D+17

S14AAF  IFAIL  = 1 if X > 1.70D+2
        IFAIL  = 2 if X < -1.70D+2
        IFAIL  = 3 if abs(X) < 2.23D-308
S14ABF  IFAIL  = 2 if X > 2.55D+305

S15ADF  x(hi)  = 2.66D+1
        x(low) = -6.25D+0
S15AEF  x(hi)  = 6.25D+0

S17ACF  IFAIL  = 1 if X > 1.0D+16
S17ADF  IFAIL  = 1 if X > 1.0D+16
        IFAIL  = 3 if 0.0D+00 < X <= 2.23D-308
S17AEF  IFAIL  = 1 if abs(X) > 1.0D+16
S17AFF  IFAIL  = 1 if abs(X) > 1.0D+16
S17AGF  IFAIL  = 1 if X > 1.038D+2
        IFAIL  = 2 if X < -5.6D+10
S17AHF  IFAIL  = 1 if X > 1.041D+2
        IFAIL  = 2 if X < -5.6D+10
S17AJF  IFAIL  = 1 if X > 1.041D+2
        IFAIL  = 2 if X < -1.8D+9
S17AKF  IFAIL  = 1 if X > 1.041D+2
        IFAIL  = 2 if X < -1.8D+9
S17DCF  IFAIL  = 2 if abs (Z) < 3.93D-305
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
S17DEF  IFAIL  = 2 if imag (Z) > 7.00D+2
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 1.07D+9
S17DGF  IFAIL  = 3 if abs (Z) > 1.02D+3
        IFAIL  = 4 if abs (Z) > 1.04D+6
S17DHF  IFAIL  = 3 if abs (Z) > 1.02D+3
        IFAIL  = 4 if abs (Z) > 1.04D+6
S17DLF  IFAIL  = 2 if abs (Z) < 3.93D-305
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9

S18ADF  IFAIL  = 2 if 0.0D+00 < X <= 2.23D-308
S18AEF  IFAIL  = 1 if abs(X) > 7.116D+2
S18AFF  IFAIL  = 1 if abs(X) > 7.116D+2
S18CDF  IFAIL  = 2 if 0.0D+00 < X <= 2.23D-308
S18DCF  IFAIL  = 2 if abs (Z) < 3.93D-305
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
S18DEF  IFAIL  = 2 if real (Z) > 7.00D+2
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 1.07D+9

S19AAF  IFAIL  = 1 if abs(x) >= 4.95000D+1
S19ABF  IFAIL  = 1 if abs(x) >= 4.95000D+1
S19ACF  IFAIL  = 1 if X > 9.9726D+2
S19ADF  IFAIL  = 1 if X > 9.9726D+2

S21BCF  IFAIL  = 3 if an argument < 1.579D-205
        IFAIL  = 4 if an argument >= 3.774D+202
S21BDF  IFAIL  = 3 if an argument < 2.820D-103
        IFAIL  = 4 if an argument >= 1.404D+102

X01

The values of the mathematical constants are:

X01AAF (PI)    = 3.1415926535897932D+00
X01ABF (GAMMA) = 0.5772156649015329D+00

X02

The values of the machine constants are:
The basic parameters of the model

X02BHF =     2
X02BJF =    53
X02BKF =  -1021
X02BLF =  1024
X02DJF =  .TRUE.

Derived parameters of the floating-point arithmetic

X02AJF = 1.11022302462516D-16 
X02AKF = 2.22507385850721D-308 
X02ALF = 1.79769313486231D+308 
X02AMF = 2.22507385850721D-308 
X02ANF = 2.22507385850721D-308

Parameters of other aspects of the computing environment

X02AHF = 1.42724769270596D+45 
X02BBF = 2147483647
X02BEF = 15
X02DAF = .FALSE.

X04
The default output units for error and advisory messages for those routines which can produce explicit output are both Fortran Unit 6.

5. Documentation

The Library Manual is supplied in the form of Portable Document Format (PDF) files, with an HTML index, in the nagdoc_mk21 directory. The introductory material is also provided as HTML files in the nagdoc_mk21 directory.

A main index file has been provided (nagdoc_mk21/html/mark21.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:

un.html - Users' Note (this document)

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 FSL6A21DPL).

(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 the following URLs:

http://www.nag.co.uk/, http://www.nag.com/ or http://www.nag-j.co.jp/

(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.

(e) Product Registration

To ensure that you receive information on updates and other relevant announcements, please register this product with us. For NAG Library products this may be accomplished by filling in the online registration form at http://www.nag.co.uk/numeric/Library_Registration.asp.

7. User Feedback

Many factors influence the way that 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 any of the NAG Response Centres (shown below).

Appendix - Contact Addresses

NAG Ltd
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Tel: +44 (0)1865 511245                 Tel: +44 (0)1865 311744
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Tel: +1 630 971 2337                    Tel: +1 630 971 2337
Fax: +1 630 971 2706                    Fax: +1 630 971 2706

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email: help@nag-j.co.jp

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

NAG SMP Library, Mark 21

FSL6A21DPL - License Managed

AMD64, Linux 64, PGI Fortran, Double Precision

Users' Note

Contents

F06, F07 and F08

G02

P01

S07 - S21

X01

X02

X04

(a) Contact with NAG

(b) NAG Response Centres

(c) NAG Websites

(d) NAG Electronic Newsletter

(e) Product Registration