NAG SMP Library, Mark 21

FSAI621DAL - License Managed

IBM POWER5, 64-bit, AIX, XLF, 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 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.

The library can be used with or without the compiler flag -qextname.

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/fsai621dal or /usr/local/NAG/fsai621dal 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 ESSL libraries, you may link in the following manner: 
  xlf_r -q64 -qsmp=omp -qnosave driver.f [INSTALL_DIR]/lib/libnagsmp.a -lesslsmp
where driver.f is your application program; or 
  xlf_r -q64 -qsmp=omp -qnosave driver.f [INSTALL_DIR]/lib/libnagsmp.so -lesslsmp
if the shareable library is required.

3.1.2. Libraries in the linker search path

In this section we assume that the NAG SMP and the ESSL 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 ESSL libraries, you may link in the following manner: 

  xlf_r -q64 -qsmp=omp -qnosave driver.f -lnagsmp -lesslsmp
This will usually link to the static library in preference to the shareable library if both the libraries are at the same location.

To use the shareable library libnagsmp.so you need the -brtl compiler flag: 

  xlf_r -q64 -qsmp=omp -qnosave -brtl driver.f -lnagsmp -lesslsmp

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

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:

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 IBM ESSL 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 IBM ESSL, except for the following routines: 

    DBDSDC    DBDSQR    DDISNA    DGBBRD    DGBCON    DGBEQU    DGBRFS    DGBSV
DGBSVX    DGBTRF    DGBTRS    DGEBAK    DGEBAL    DGEBRD    DGECON    DGEEQU
DGEES     DGEESX    DGEEV     DGEEVX    DGEHRD    DGELQF    DGELS     DGELSD
DGELSS    DGELSY    DGEQLF    DGEQP3    DGEQPF    DGEQRF    DGERFS    DGERQF
DGESDD    DGESV     DGESVD    DGESVX    DGETRF    DGETRS    DGGBAK    DGGBAL
DGGES     DGGESX    DGGEV     DGGEVX    DGGGLM    DGGHRD    DGGLSE    DGGQRF
DGGRQF    DGGSVD    DGGSVP    DGTCON    DGTRFS    DGTSV     DGTSVX    DGTTRF
DGTTRS    DHGEQZ    DHSEIN    DHSEQR    DLAGTM    DLALS0    DLALSD    DLANGT
DLANST    DLASDA    DLASDQ    DOPGTR    DOPMTR    DORGBR    DORGHR    DORGLQ
DORGQL    DORGQR    DORGRQ    DORGTR    DORMBR    DORMHR    DORMLQ    DORMQL
DORMQR    DORMRQ    DORMRZ    DORMTR    DPBCON    DPBEQU    DPBRFS    DPBSTF
DPBSV     DPBSVX    DPBTRF    DPBTRS    DPOCON    DPOEQU    DPORFS    DPOSV
DPOSVX    DPOTRF    DPOTRS    DPPCON    DPPEQU    DPPRFS    DPPSV     DPPSVX
DPPTRI    DPTCON    DPTEQR    DPTRFS    DPTSV     DPTSVX    DPTTRF    DPTTRS
DROTI     DSBEV     DSBEVD    DSBEVX    DSBGST    DSBGV     DSBGVD    DSBGVX
DSBTRD    DSPCON    DSPEV     DSPEVD    DSPEVX    DSPGST    DSPGV     DSPGVD
DSPGVX    DSPRFS    DSPSV     DSPSVX    DSPTRD    DSPTRF    DSPTRI    DSPTRS
DSTEBZ    DSTEDC    DSTEGR    DSTEIN    DSTEQR    DSTERF    DSTEV     DSTEVD
DSTEVR    DSTEVX    DSYCON    DSYEV     DSYEVD    DSYEVR    DSYEVX    DSYGST
DSYGV     DSYGVD    DSYGVX    DSYRFS    DSYSV     DSYSVX    DSYTRD    DSYTRF
DSYTRI    DSYTRS    DTBCON    DTBRFS    DTBTRS    DTGEVC    DTGEXC    DTGSEN
DTGSJA    DTGSNA    DTGSYL    DTPCON    DTPRFS    DTPTRS    DTRCON    DTREVC
DTREXC    DTRRFS    DTRSEN    DTRSNA    DTRSYL    DTRTRS    DTZRZF    ZBDSQR
ZGBBRD    ZGBCON    ZGBEQU    ZGBRFS    ZGBSV     ZGBSVX    ZGBTRF    ZGBTRS
ZGEBAK    ZGEBAL    ZGEBRD    ZGECON    ZGEEQU    ZGEES     ZGEESX    ZGEEV
ZGEEVX    ZGEHRD    ZGELQF    ZGELS     ZGELSD    ZGELSS    ZGELSY    ZGEQLF
ZGEQP3    ZGEQPF    ZGEQRF    ZGERFS    ZGERQF    ZGESDD    ZGESV     ZGESVD
ZGESVX    ZGETRF    ZGETRS    ZGGBAK    ZGGBAL    ZGGES     ZGGESX    ZGGEV
ZGGEVX    ZGGGLM    ZGGHRD    ZGGLSE    ZGGQRF    ZGGRQF    ZGGSVD    ZGGSVP
ZGTCON    ZGTRFS    ZGTSV     ZGTSVX    ZGTTRF    ZGTTRS    ZHBEV     ZHBEVD
ZHBEVX    ZHBGST    ZHBGV     ZHBGVD    ZHBGVX    ZHBTRD    ZHECON    ZHEEV
ZHEEVD    ZHEEVR    ZHEEVX    ZHEGST    ZHEGV     ZHEGVD    ZHEGVX    ZHERFS
ZHESV     ZHESVX    ZHETRD    ZHETRF    ZHETRI    ZHETRS    ZHGEQZ    ZHPCON
ZHPEV     ZHPEVD    ZHPEVX    ZHPGST    ZHPGV     ZHPGVD    ZHPGVX    ZHPRFS
ZHPSV     ZHPSVX    ZHPTRD    ZHPTRF    ZHPTRI    ZHPTRS    ZHSEIN    ZHSEQR
ZLAGTM    ZLALS0    ZLALSD    ZLANGT    ZLANHT    ZPBCON    ZPBEQU    ZPBRFS
ZPBSTF    ZPBSV     ZPBSVX    ZPBTRF    ZPBTRS    ZPOCON    ZPOEQU    ZPORFS
ZPOSV     ZPOSVX    ZPOTRF    ZPOTRS    ZPPCON    ZPPEQU    ZPPRFS    ZPPSV
ZPPSVX    ZPPTRF    ZPPTRI    ZPPTRS    ZPTCON    ZPTEQR    ZPTRFS    ZPTSV
ZPTSVX    ZPTTRF    ZPTTRS    ZSPCON    ZSPMV     ZSPRFS    ZSPSV     ZSPSVX
ZSPTRF    ZSPTRI    ZSPTRS    ZSTEDC    ZSTEGR    ZSTEIN    ZSTEQR    ZSYCON
ZSYMV     ZSYRFS    ZSYSV     ZSYSVX    ZSYTRF    ZSYTRI    ZSYTRS    ZTBCON
ZTBRFS    ZTBTRS    ZTGEVC    ZTGEXC    ZTGSEN    ZTGSJA    ZTGSNA    ZTGSYL
ZTPCON    ZTPRFS    ZTPTRS    ZTRCON    ZTREVC    ZTREXC    ZTRRFS    ZTRSEN
ZTRSNA    ZTRSYL    ZTRTRS    ZTZRZF    ZUNGBR    ZUNGHR    ZUNGLQ    ZUNGQL
ZUNGQR    ZUNGRQ    ZUNGTR    ZUNMBR    ZUNMHR    ZUNMLQ    ZUNMQL    ZUNMQR
ZUNMRQ    ZUNMRZ    ZUNMTR    ZUPGTR    ZUPMTR

    The following NAG named routines are wrappers to call LAPACK routines from the vendor library: 
    F07GDF    F07GEF

  2. G02

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

  3. P01

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

  4. S07 - S21

    Functions in this chapter will give error messages if called with illegal or unsafe arguments. The constants referred to in the 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

  5. X01

    The values of the mathematical constants are: 
    X01AAF (PI)    = 3.1415926535897932D+00
X01ABF (GAMMA) = 0.5772156649015329D+00

  6. 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 = 8.11296384146067D+31 
X02BBF = 2147483647
X02BEF = 15
X02DAF = .FALSE.

  7. 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

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