NAG SMP Library, Mark 21

FSFL621DA

Fujitsu HX600, Linux 64, Fujitsu Fortran, Double Precision

Users' Note



Contents


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 library supplied with this implementation has been compiled in a manner that facilitates the use of the OpenMP threading model. Lower-level threading models such as Pthreads are not supported.

2. Post Release Information

Please check the following URL: Post Release Information for details of any new information related to the applicability or usage of this implementation.

3. General Information

3.1. Accessing the Library

This section shows two ways of accessing the NAG SMP Library depending on the location of the compiled library.

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/fsfl621da or /usr/local/NAG/fsfl621da depending on your system; however it could have been changed by the installer. To identify [INSTALL_DIR] for this installation:

To use the NAG SMP and the SSL II libraries, you may link in the following manner:
  frt -X9 -fw -Kthreadsafe -KOMP driver.f [INSTALL_DIR]/lib/libnagsmp.a -SSL2BLAMP 
where driver.f is your application program.

To use the interface blocks provided (see Section 3.5) you need to replace frt in the above command by frt -Am -Ipathname, where pathname ([INSTALL_DIR]/nag_interface_blocks) is the path of the directory containing the compiled interface blocks.

3.1.2. Libraries in the linker search path

In this section we assume that the NAG SMP and the SSL II libraries are installed in, or are pointed at by symbolic links from, directories in the search path of the linker, such as /usr/lib/sparcv9.

To use the NAG SMP and the SSL II libraries, you may link in the following manner:

  frt -X9 -fw -Kthreadsafe -KOMP driver.f -lnagsmp -SSL2BLAMP
where driver.f is your application program.

To use the interface blocks provided (see Section 3.5) you need to replace frt in the above command by frt -Am -Ipathname, where pathname ([INSTALL_DIR]/nag_interface_blocks) is the path of the directory containing the compiled interface blocks.

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 a script nagsmp_example.

The example programs are most easily accessed by the command nagsmp_example, to link with the NAG static library libnagsmp.a and the SSL II 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, redirecting its output to a file.

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 using 4 OpenMP threads 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 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 -Am and -Ipathname options on each compiler 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:

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.
  1. 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 the thread-parallel version of the Fujitsu Scientific Subroutine Library "SSL II" 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 the thread-parallel version of the Fujitsu Scientific Subroutine Library "SSL II", except for the following routines (including some utilities):

    DBDSDC    DBDSQR    DDOT      DGBRFS    DGBSV     DGBSVX    DGBTRF    DGBTRS
    DGEBAL    DGEBRD    DGEES     DGEESX    DGEEV     DGEEVX    DGELS     DGELSD
    DGELSS    DGELSY    DGEMV     DGEQP3    DGEQRF    DGERFS    DGESDD    DGESV
    DGESVD    DGESVX    DGETRF    DGETRS    DGGES     DGGESX    DGGEV     DGGEVX
    DGGGLM    DGGLSE    DGGQRF    DGGRQF    DGTRFS    DGTSVX    DHSEIN    DLALSD
    DLASDA    DLASDQ    DOPGTR    DORGBR    DORGHR    DORGQR    DORGTR    DORMBR
    DORMHR    DORMQR    DORMTR    DPBRFS    DPBSV     DPBSVX    DPBTRS    DPORFS
    DPOSV     DPOSVX    DPOTRF    DPOTRS    DPPRFS    DPPSV     DPPSVX    DPPTRS
    DPTCON    DPTEQR    DPTRFS    DPTSVX    DSBEV     DSBEVD    DSBEVX    DSBGV
    DSBGVD    DSBGVX    DSBTRD    DSPEV     DSPEVD    DSPEVX    DSPGV     DSPGVD
    DSPGVX    DSPRFS    DSPSVX    DSTEBZ    DSTEDC    DSTEGR    DSTEIN    DSTEQR
    DSTEV     DSTEVD    DSTEVR    DSTEVX    DSYEV     DSYEVD    DSYEVR    DSYEVX
    DSYGV     DSYGVD    DSYGVX    DSYRFS    DSYSV     DSYSVX    DSYTRD    DTBRFS
    DTBTRS    DTPRFS    DTPTRS    DTRRFS    ZBDSQR    ZGBRFS    ZGBSV     ZGBSVX
    ZGBTRF    ZGBTRS    ZGEBAL    ZGEBRD    ZGEES     ZGEESX    ZGEEV     ZGEEVX
    ZGELS     ZGELSD    ZGELSS    ZGELSY    ZGEQP3    ZGEQRF    ZGERFS    ZGESDD
    ZGESV     ZGESVD    ZGESVX    ZGETRF    ZGETRS    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    ZHESV     ZHESVX
    ZHETRD    ZHPEV     ZHPEVD    ZHPEVX    ZHPGV     ZHPGVD    ZHPGVX    ZHPRFS
    ZHPSVX    ZHSEIN    ZLALSD    ZPBRFS    ZPBSV     ZPBSVX    ZPBTRS    ZPORFS
    ZPOSV     ZPOSVX    ZPOTRF    ZPOTRS    ZPPRFS    ZPPSV     ZPPSVX    ZPPTRS
    ZPTEQR    ZPTRFS    ZPTSVX    ZSPRFS    ZSPSVX    ZSTEDC    ZSTEGR    ZSTEIN
    ZSTEQR    ZSYCON    ZSYRFS    ZSYSV     ZSYSVX    ZSYTRF    ZTBRFS    ZTBTRS
    ZTPRFS    ZTPTRS    ZTRRFS    ZUNGBR    ZUNGHR    ZUNGQR    ZUNGTR    ZUNMBR
    ZUNMHR    ZUNMQR    ZUNMTR    ZUPGTR
    

    The following NAG named routines are wrappers to call LAPACK routines from the vendor library:
    F08PEF    F08PSF
    

  2. G02
  3. The value of ACC, the machine-dependent constant mentioned in several documents in the chapter, is 1.0D-13.

  4. P01
  5. On hard failure, P01ABF writes the error message to the error message unit specified by X04AAF and then stops.
  6. 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)  = 2.2D+15
    S13ADF  x(hi)  = 2.2D+15
    
    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 > 2.2D+15
    S17ADF  IFAIL  = 1 if X > 2.2D+15
            IFAIL  = 3 if 0.0D+00 < X <= 2.23D-308
    S17AEF  IFAIL  = 1 if abs(X) > 2.2D+15
    S17AFF  IFAIL  = 1 if abs(X) > 2.2D+15
    S17AGF  IFAIL  = 1 if X > 1.038D+2
            IFAIL  = 2 if X < -2.2D+10
    S17AHF  IFAIL  = 1 if X > 1.041D+2
            IFAIL  = 2 if X < -2.2D+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
    
  7. X01

    The values of the mathematical constants are:
    X01AAF (PI)    = 3.1415926535897932D+00
    X01ABF (GAMMA) = 0.5772156649015329D+00
    
  8. 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 = 4.45014771701441D-308 
    
    Parameters of other aspects of the computing environment
    X02AHF = 2.25179981368524D+15 
    X02BBF = 2147483647
    X02BEF = 15
    X02DAF = .FALSE.
    
  9. 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:

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 FSFL621DA).

(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/

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7. User Feedback

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Appendix - Contact Addresses

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