NAG Fortran Library, Mark 22

FLW3222DCL - License Managed

Windows XP/Vista, Intel Visual Fortran

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 Mark 22 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 been compiled in a manner that facilitates the use of multiple threads.

2. Post Release Information

Please check the following URL:

http://www.nag.co.uk/doc/inun/fl22/w32dcl/postrelease.html

for details of any new information related to the applicability or usage of this implementation.

3. General Information

For best performance, we recommend that you should use the variant of the NAG Fortran Library which is based on the supplied Math Kernel Library (MKL) i.e. nag_mkl_MT.lib, nag_mkl_MD.lib or FLW3222DC_mkl.lib/FLW3222DC_mkl.dll. However if you use a version of the MKL different from the version used in creating this implementation and you have problems when calling a NAG routine, we suggest that you use one of the above libraries with the supplied MKL, or one of the self-contained libraries nag_nag_MT.lib, nag_nag_MD.lib or FLW3222DC_nag.lib/FLW3222DC_nag.dll.

This implementation of the NAG Library is appropriate for use with the compilers described in Section 2.1 of the Installer's Note. Although it contains DLL versions of the NAG Library these are not intended for use from other packages and environments such as Visual Basic or Excel; see the post release information page on our website (described in Section 2 above) for further details.

3.1. Accessing the Library

In this section we assume that the Library has been installed in the default folder:

  c:\Program Files\NAG\FL22\flw3222dcl
If this folder does not exist, please consult the system manager (or the person who did the installation). In some of the following subsections, this folder is referred to as install dir.

We also assume that the default shortcut for the Library command prompt is placed in the Start Menu under:

  Start|All Programs|NAG|FL22|

If this shortcut does not exist, please consult the system manager (or the person who did the installation).

If you are using one of the DLL forms of the Library (see Section 3.1.1), you need to ensure that the NAG DLL (FLW3222DC_mkl.dll or FLW3222DC_nag.dll) is accessible at run time; therefore the install dir\bin folder must be on the path. If an MKL-based version of the Library is to be used, the install dir\MKL_ia32_10.1\bin folder must also be on the path, but should appear later in the path than the install dir\bin folder, since the NAG versions of a few BLAS/LAPACK routines are included in the NAG Libraries to avoid problems with the vendor versions. (See Section 4 for details.) Note that the Intel Fortran run-time libraries libifcoremd.dll and libmmd.dll are expected to be accessible via the path too. If they are not, you may run the batch file ifort_rtls.bat in the install dir\bin folder to make the Intel Fortran 10.1 version of these files available from that folder.

To check the accessibility of the NAG DLLs, run the program NAG_Fortran_DLL_info.exe which is available from the Start Menu shortcut

  Start|All Programs|NAG|FL22|NAG Fortran Library -
      Intel Fortran (FLW3222DCL). Check Accessibility
See Section 4.2.3 of the Installer's Note for details of this utility.

3.1.1. From a command window

To access this implementation from a command window some environment variables need to be set.

The shortcut:

  Start|All Programs|NAG|FL22|NAG Fortran Library -
      Intel Fortran (FLW3222DCL). Command Prompt

may be used to start a command prompt window with the correct settings for the INCLUDE, LIB and PATH environment variables for the Library and the supplied MKL.

If the shortcut is not used, you can set the environment variables by running the batch file envvars.bat for this implementation. The default location of this file is:

  c:\Program Files\NAG\FL22\flw3222dcl\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw3222dcl.

You may then compile and link to the NAG Fortran Library on the command line using one of the following commands:

  ifort /MT driver.f nag_mkl_MT.lib user32.lib libguide.lib
      mkl_intel_c.lib mkl_intel_thread.lib mkl_core.lib

  ifort /MT driver.f nag_nag_MT.lib user32.lib

  ifort /MD driver.f nag_mkl_MD.lib user32.lib libguide40.lib
      mkl_intel_c_dll.lib mkl_intel_thread_dll.lib mkl_core_dll.lib

  ifort /MD driver.f nag_nag_MD.lib user32.lib

  ifort /MD driver.f FLW3222DC_mkl.lib libguide40.lib
      mkl_intel_c_dll.lib mkl_intel_thread_dll.lib mkl_core_dll.lib

  ifort /MD driver.f FLW3222DC_nag.lib
where driver.f is your application program. Note that each command should be issued on a single line; some of the commands are shown split over two lines here to avoid truncation if this note is printed. The order of the libraries is important because certain parts of the MKL should not be used (see Section 4).

The first two commands use libraries compiled with the /MT option. The first command will use the static library without the NAG version of the BLAS/LAPACK procedures (nag_mkl_MT.lib) and the MKL static libraries. The second command will use the library with the NAG version of the BLAS/LAPACK procedures (nag_nag_MT.lib). The option /MT must be used to ensure linking with the correct run-time libraries (multithreaded static run-time libraries in this case).

The third and fourth commands use static libraries compiled with the /MD option. The third command will use the static library without the NAG version of the BLAS/LAPACK procedures (nag_mkl_MD.lib) and the MKL DLLs. The fourth command will use the library with the NAG version of the BLAS/LAPACK procedures (nag_nag_MD.lib). The option /MD must be used to ensure linking with the correct run-time libraries (multithreaded dynamic link run-time libraries in this case).

The last two commands use DLL import libraries compiled with the /MD option. The fifth command will use the DLL without the NAG version of the BLAS/LAPACK procedures (FLW3222DC_mkl.lib) and the MKL DLLs. The last command will use the DLL with the NAG version of the BLAS/LAPACK procedures (FLW3222DC_nag.lib). The option /MD must be used to ensure linking with the correct run-time libraries.

Note that /MT is equivalent to specifying /libs:static /threads and /MD is equivalent to specifying /libs:dll /threads.

If your program uses multiple threads, you should also compile with the /automatic option, e.g.:

  ifort /MT /automatic driver.f nag_mkl_MT.lib user32.lib libguide.lib
      mkl_intel_c.lib mkl_intel_thread.lib mkl_core.lib

Please note that the Intel Visual Fortran compiler environment variables must be set in the command window. For more details refer to the User's Guide for the compiler.

3.1.2. From MS Visual Studio .NET

Once Visual Studio has been opened, it is possible to set up the directories for use with Intel Fortran in this and all subsequent projects which use this compiler. One way to do so is:
  1. Select the Tools pull down menu, and click on Options.
  2. In the Options window, click on Intel(R) Fortran (or Intel(R) Visual Fortran) and then choose Compilers in the left window pane. (In some versions of Visual Studio you may need to click on Show all settings to see the Intel compiler options.)
  3. In the right window pane, click on the '...' to the right of the Libraries panel.
  4. Add the path to the NAG static or DLL import library to the Set Directory List window. The default location is:
    "c:\Program Files\NAG\FL22\flw3222dcl\lib"
  5. If you intend to use the MKL libraries then you need to add the path to the MKL static or DLL import libraries after the path to the NAG Library. The default location is:
    "c:\Program Files\NAG\FL22\flw3222dcl\MKL_ia32_10.1\lib"
  6. Click on the OK button in the Set Directory List window.
  7. In the right window pane, click on the '...' to the right of the Includes panel.
  8. Add the path to the NAG interface blocks to the Set Directory List window. The default location is:
    "c:\Program Files\NAG\FL22\flw3222dcl\nag_interface_blocks"
  9. Click on the OK button in the Set Directory List window.
  10. Click on the OK button in the Options window.
Having done this, if an Intel Fortran project requires a library or NAG interface block during the compilation and linking process then the full path to the library and interface block do not need to be specified.

The interface block is simply accessed by inserting a USE statement as described in greater detail in Section 3.2.

Whilst the above changes will apply to every Intel Fortran project, the following tasks need to be performed for each individual Intel Fortran project.

The library is intended to be run in fully optimised mode, so to avoid any warning messages, you might decide to set the active configuration to Release. You can do this from the Toolbar or alternatively via the Build|Configuration Manager menus. Note that if you work in Debug mode, you may receive a warning message about conflicting C run-time libraries.

There are a number of ways to add the NAG Library to the project. We describe just two; choose the one that most suits you.

If the Solution Explorer window is open then make sure that group project (the first line) is NOT selected. From the Project menu, choose the project Properties item. (Alternatively right-click on a specific single project in the Solution Explorer and choose Properties.)

From the form, click Linker in the leftmost panel and then choose Input. The right hand panel will now have an Additional Dependencies entry, and you need to type nag_mkl_MT.lib user32.lib libguide.lib mkl_intel_c.lib mkl_intel_thread.lib mkl_core.lib in this location to use the nag_mkl_MT.lib library and MKL. Please note that the six libraries are separated by a space only and that nag_mkl_MT.lib must be the first one. Press the OK button. If you wish to use the self-contained NAG Library nag_nag_MT.lib then you need to add nag_nag_MT.lib user32.lib instead of the six libraries above. Similary, to use one of the other NAG Libraries, insert the appropriate library or libraries (as detailed in Section 3.1.1) in the Additional Dependencies field.

The Properties information may also be accessed via the Toolbar. With the project selected in Solution Explorer, choose the Properties Window button on the Toolbar. In the ensuing window choose then the rightmost Property Pages icon. As in the paragraph above, from the form click Linker in the leftmost panel and then choose Input. The right hand panel will now have an Additional Dependencies entry, and you need to type the names of the relevant libraries in this location.

Before you can compile the project you need to specify the correct run-time library needed. From the Properties Window, click Fortran in the leftmost panel and then choose Libraries. The right hand panel will now have a Runtime Library entry, and you need to select Multithreaded if your project uses one of the two libraries nag_nag_MT.lib or nag_mkl_MT.lib. If your projects uses any of the other NAG libraries you need to select Multithreaded DLL. After you select the correct run-time library press the OK button.

For a multithreaded application, as well as selecting a multithreaded run-time library, you should set the /automatic (or /Qauto) compiler flag, to ensure that all local variables are allocated on the stack. To set this option, from the Properties form click Fortran and then choose Data. Click on the Local Variable Storage entry in the right hand panel and select Local Variables AUTOMATIC from the drop-down list. Press the OK button to accept the changes and close the form.

In summary the setting of the project Additional Dependencies, the project Runtime Library and the PATH environment variable must be consistent as follows:

The project should now compile and link using the appropriate choice from the Build menu.

To run a program that does not require input or output redirected from standard input or standard output, from within the Microsoft Development Environment, the program may be executed via the Debug menu (by selecting Start Without Debugging, for example).

If a data file needs to be attached to the standard input or the output of a program needs to be redirected to the standard output, we recommend that you run the executable from a command prompt window to avoid the limitations of Visual Studio .NET.

3.1.3. Accessibility Check

To check whether the DLLs included in this library implementation are accessible from the current environment, run the program NAG_Fortran_DLL_info.exe which is available from the Start Menu shortcut
  Start|All Programs|NAG|FL22|NAG Fortran Library -
      Intel Fortran (FLW3222DCL). Check Accessibility
See Section 4.2.3 of the Installer's Note for details of this utility.

Note that this program should be closed after use (by pressing a key to dismiss the window), otherwise performance may be impared.

3.2. 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 programs. Their purpose is to allow the Fortran 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; and
(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).

If you use the Library command prompt shortcut or set the environment variables by running the batch file envvars.bat for this implementation (see Section 3.1.1), you can use any of the commands described in Section 3.1.1 to access these modules since the environment variable INCLUDE will be set.

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 Fortran 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
*     Mark 14 Revised. NAG Copyright 1989.
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_D_CHAPTER, ONLY: D01DAF
*                                                   *
*****************************************************
*     .. Parameters ..
      INTEGER          NOUT
      PARAMETER        (NOUT=6)
*     .. Local Scalars ..
      DOUBLE PRECISION ABSACC, ANS, YA, YB
      INTEGER          IFAIL, NPTS
*     .. External Functions ..
      DOUBLE PRECISION FA, FB, PHI1, PHI2A, PHI2B
      EXTERNAL         FA, FB, PHI1, PHI2A, PHI2B
*     .. External Subroutines ..
******************************************************
* EXTERNAL declarations need to be removed.          *
*     EXTERNAL         D01DAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      WRITE (NOUT,*) 'D01DAF Example Program Results'
      YA = 0.0D0
      YB = 1.0D0
      ABSACC = 1.0D-6
      WRITE (NOUT,*)
      IFAIL = 1
*
      CALL D01DAF(YA,YB,PHI1,PHI2A,FA,ABSACC,ANS,NPTS,IFAIL)
*
      IF (IFAIL.LT.0) THEN
         WRITE (NOUT,99998) ' ** D01DAF returned with IFAIL = ', IFAIL
      ELSE
*
         WRITE (NOUT,*) 'First formulation'
         WRITE (NOUT,99999) 'Integral =', ANS
         WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
         IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
         WRITE (NOUT,*)
         WRITE (NOUT,*) 'Second formulation'
         IFAIL = 1
*
         CALL D01DAF(YA,YB,PHI1,PHI2B,FB,ABSACC,ANS,NPTS,IFAIL)
*
         WRITE (NOUT,99999) 'Integral =', ANS
         WRITE (NOUT,99998) 'Number of function evaluations =', NPTS
         IF (IFAIL.GT.0) WRITE (NOUT,99998) 'IFAIL = ', IFAIL
      END IF
*
99999 FORMAT (1X,A,F9.4)
99998 FORMAT (1X,A,I5)
      END
*
      DOUBLE PRECISION FUNCTION PHI1(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION Y
*     .. Executable Statements ..
      PHI1 = 0.0D0
      RETURN
      END
*
      DOUBLE PRECISION FUNCTION PHI2A(Y)
*     .. Scalar Arguments ..
      DOUBLE PRECISION Y
*     .. Intrinsic Functions ..
      INTRINSIC        SQRT
*     .. Executable Statements ..
      PHI2A = 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 PHI2B(Y)
*****************************************************
* Add USE statements for relevant chapters          *
      USE NAG_F77_X_CHAPTER, ONLY: X01AAF
*                                                   *
*****************************************************
*     .. Scalar Arguments ..
      DOUBLE PRECISION Y
*     .. External Functions ..
******************************************************
* Function Type declarations need to be removed.     *
*     DOUBLE PRECISION X01AAF
*                                                    *
******************************************************
******************************************************
* EXTERNAL declarations need to be removed.          *
*     EXTERNAL         X01AAF
*                                                    *
******************************************************
*     .. Executable Statements ..
      PHI2B = 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

Modified versions of all the example program source files, which use the modules, are available in the zip file source_interface_blocks.zip. This can be found in the folder install dir\examples.

3.3. Example Programs

The example results distributed were generated at Mark 22, using the software described in Section 2.2 of the Installer's Note. These example results may not be exactly reproducible if the example programs are run in a slightly different environment (for example, a different Fortran compiler, a different compiler library, or a different set of BLAS or LAPACK routines). The results which are most sensitive to such differences are: eigenvectors (which may differ by a scalar multiple, often -1, but sometimes complex); numbers of iterations and function evaluations; and residuals and other "small" quantities of the same order as the machine precision.

Note that the example material has been adapted, if necessary, from that published in the Library Manual, so that programs are suitable for execution with this implementation with no further changes. The distributed example programs should be used in preference to the versions in the Library Manual wherever possible.

The example programs are most easily accessed by one of the following batch files:

nag_mkl_MT.lib and nag_nag_MT.lib use the static multithreaded run-time library, whilst nag_mkl_MD.lib, nag_nag_MD.lib, FLW3222DC_mkl.lib and FLW3222DC_nag.lib use the multithreaded DLL run-time library.

The batch files need the environment variable NAG_FLW3222DCL.

As mentioned in Section 3.1.1, the installation procedure provides a shortcut which starts a Command Prompt with local environment variables. The environment variables include NAG_FLW3222DCL. This shortcut is, by default, placed in the Start Menu under

  Start|All Programs|NAG|FL22|NAG Fortran Library -
      Intel Fortran (FLW3222DCL). Command Prompt
If the shortcut is not used, you need to set this environment variable. It can be set by running the batch file envvars.bat for this implementation. The default location of this file is:
  c:\Program Files\NAG\FL22\flw3222dcl\batch\envvars.bat
If the file is not in the default location, you can locate it by searching for the file envvars.bat containing flw3222dcl.

Each of the nag_example* batch files mentioned above 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, writing its output to a file.

The example program concerned is specified by the argument to the command, e.g.

  nag_example_mkl_MT e04ucf
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 distributed example results are those obtained with the static library nag_mkl_MD.lib, (using the MKL BLAS and LAPACK routines). Running the examples with the self-contained library (using the NAG BLAS and LAPACK routines) may give slightly different results.

3.4. Interpretation of Bold Italicised Terms

In order to support all implementations of the Library, the Manual has adopted a convention of using bold italics to distinguish terms which have different interpretations in different implementations.

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

real                  means REAL
double precision      means DOUBLE PRECISION
complex               means COMPLEX
complex*16            means COMPLEX*16 (or equivalent)
basic precision       means DOUBLE PRECISION
additional precision  means quadruple precision
reduced precision     means REAL

Another important bold italicised term is machine precision, which denotes the relative precision to which double precision floating-point numbers are stored in the computer, e.g. in an implementation with approximately 16 decimal digits of precision, machine precision has a value of approximately 1.0D-16.

The precise value of machine precision is given by the routine X02AJF. Other routines in Chapter X02 return the values of other implementation-dependent constants, such as the overflow threshold, or the largest representable integer. Refer to the X02 Chapter Introduction for more details.

The bold italicised term block size is used only in Chapters F07 and F08. It denotes the block size used by block algorithms in these chapters. You only need to be aware of its value when it affects the amount of workspace to be supplied – see the parameters WORK and LWORK of the relevant routine documents and the Chapter Introduction.

3.5. Explicit Output from NAG Routines

Certain routines produce explicit error messages and advisory messages via output units which have default values that 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.

4. Routine-specific Information

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

  1. D06

    When running some routines in this chapter you may need to increase the stack size to avoid a stack overflow exception. One way of doing this is to use a command such as
      ifort /MT driver.f nag_nag_MT.lib user32.lib /link /stack:128000000
    
    which will pass the specified stack size to the linker.

  2. F06, F07 and F08

    In Chapters F06, F07 and F08, alternate routine names are available for BLAS and LAPACK derived routines. For details of the alternate routine names please refer to the relevant Chapter Introduction. Note that applications should reference routines by their BLAS/LAPACK names, rather than their NAG-style names, for optimum performance.

    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 MKL may require a different amount of workspace from the equivalent NAG versions of these routines. Care should be taken when using the workspace query mechanism.

    In this implementation calls to the NAG version of the following Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) are included in the libraries nag_mkl_MT.lib, nag_mkl_MD.lib and FLW3222DC_mkl.dll to avoid problems with the vendor version:

      DGGGLM     DGGLSE     ZGELS      ZGGGLM     ZGGLSE
    

  3. G02

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

  4. P01

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

  5. 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   = 1.0E+13
            F_2   = 1.0E-14
    
    S10AAF  E_1   = 1.8715E+1
    S10ABF  E_1   = 7.080E+2
    S10ACF  E_1   = 7.080E+2
    
    S13AAF  X_hi  = 7.083E+2
    S13ACF  X_hi  = 1.0E+16
    S13ADF  X_hi  = 1.0E+17
    
    S14AAF  IFAIL  = 1 if X > 1.70E+2
            IFAIL  = 2 if X < -1.70E+2
            IFAIL  = 3 if abs(X) < 2.23E-308
    S14ABF  IFAIL  = 2 if X > X_big = 2.55E+305
    
    S15ADF  X_hi  = 2.65E+1
    S15AEF  X_hi  = 2.65E+1
    S15AFF  underflow trap was necessary
    S15AGF  IFAIL  = 1 if X >= 2.53E+307
            IFAIL  = 2 if 4.74E+7 <= X < 2.53E+307
            IFAIL  = 3 if X < -2.66E+1
    
    S17ACF  IFAIL  = 1 if X > 1.0E+16
    S17ADF  IFAIL  = 1 if X > 1.0E+16
            IFAIL  = 3 if 0.0E0 < X <= 2.23E-308
    S17AEF  IFAIL  = 1 if abs(X) > 1.0E+16
    S17AFF  IFAIL  = 1 if abs(X) > 1.0E+16
    S17AGF  IFAIL  = 1 if X > 1.038E+2
            IFAIL  = 2 if X < -5.7E+10
    S17AHF  IFAIL  = 1 if X > 1.041E+2
            IFAIL  = 2 if X < -5.7E+10
    S17AJF  IFAIL  = 1 if X > 1.041E+2
            IFAIL  = 2 if X < -1.9E+9
    S17AKF  IFAIL  = 1 if X > 1.041E+2
            IFAIL  = 2 if X < -1.9E+9
    S17DCF  IFAIL  = 2 if abs(Z) < 3.92223E-305
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
    S17DEF  IFAIL  = 2 if imag(Z) > 7.00921E+2
            IFAIL  = 3 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 1.07374E+9
    S17DGF  IFAIL  = 3 if abs(Z) > 1.02399E+3
            IFAIL  = 4 if abs(Z) > 1.04857E+6
    S17DHF  IFAIL  = 3 if abs(Z) > 1.02399E+3
            IFAIL  = 4 if abs(Z) > 1.04857E+6
    S17DLF  IFAIL  = 2 if abs(Z) < 3.92223E-305
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
    
    S18ADF  IFAIL  = 2 if 0.0E0 < X <= 2.23E-308
    S18AEF  IFAIL  = 1 if abs(X) > 7.116E+2
    S18AFF  IFAIL  = 1 if abs(X) > 7.116E+2
    S18DCF  IFAIL  = 2 if abs(Z) < 3.92223E-305
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 5 if abs(Z) or FNU+N-1 > 1.07374E+9
    S18DEF  IFAIL  = 2 if real(Z) > 7.00921E+2
            IFAIL  = 3 if abs(Z) or FNU+N-1 > 3.27679E+4
            IFAIL  = 4 if abs(Z) or FNU+N-1 > 1.07374E+9
    
    S19AAF  IFAIL  = 1 if abs(X) >= 5.04818E+1
    S19ABF  IFAIL  = 1 if abs(X) >= 5.04818E+1
    S19ACF  IFAIL  = 1 if X > 9.9726E+2
    S19ADF  IFAIL  = 1 if X > 9.9726E+2
    
    S21BCF  IFAIL  = 3 if an argument < 1.583E-205
            IFAIL  = 4 if an argument >= 3.765E+202
    S21BDF  IFAIL  = 3 if an argument < 2.813E-103
            IFAIL  = 4 if an argument >= 1.407E+102
    

  6. X01

    The values of the mathematical constants are:
    X01AAF (pi)    = 3.1415926535897932
    X01ABF (gamma) = 0.5772156649015328
    

  7. 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 = 1.11022302462516E-16
    X02AKF = 2.22507385850721E-308
    X02ALF = 1.79769313486231E+308
    X02AMF = 2.22507385850721E-308
    X02ANF = 2.22507385850721E-308
    
    Parameters of other aspects of the computing environment
    X02AHF = 1.42724769270596E+45
    X02BBF = 2147483647
    X02BEF = 15
    X02DAF = .TRUE.
    

  8. 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 available as a separate installation, via download from the NAG website, or from the distribution CD if you have one. It is also available directly on the CD. The most up-to-date version of the documentation is accessible via the NAG website at http://www.nag.co.uk/numeric/FL/FLdocumentation.asp.

The Library Manual is supplied in the following formats:

The following main index files have been provided for these formats:

	nagdoc_fl22\xhtml\FRONTMATTER\manconts.xml
	nagdoc_fl22\pdf\FRONTMATTER\manconts.pdf
	nagdoc_fl22\html\FRONTMATTER\manconts.html
If the Library Manual has been installed locally, these index files are available from the Start Menu under
  Start|All Programs|NAG|FL22|NAG Fortran Library Manual (XHTML + MathML)
  Start|All Programs|NAG|FL22|NAG Fortran Library Manual (PDF)
  Start|All Programs|NAG|FL22|NAG Fortran Library Manual (PDF + HTML Index)
respectively, by default. Use your web browser to navigate from here.

Advice on viewing and navigating the formats available can be found in the Online Documentation document.

Note that if you are using Internet Explorer, all links within the XHTML/MathML version to example source, data and results files and PDF files will be diverted from the local file system to the NAG website to avoid security restrictions which prevent the display of these pages. If you are using any other browser then local links to examples and PDF files are retained.

In addition the following are provided:

The latter is available from the Start Menu under
  Start|All Programs|NAG|FL22|NAG Fortran Library -
      Intel Fortran (FLW3222DCL). Users' Note
by default.

6. Support from NAG

(a) Contact with NAG

Queries concerning this document or the implementation generally should be directed to NAG 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 FLW3222DCL).

(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 announcements about new products or product/service enhancements, technical tips, 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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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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Suite 185
Lisle, IL  60532-4332                   NAG Inc Response Center
USA                                     email: support@nag.com

Tel: +1 630 971 2337                    Tel: +1 630 971 2337
Fax: +1 630 971 2706                    Fax: +1 630 971 2706

Nihon NAG KK
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4-9-9
Hatchobori
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Tokyo
104-0032
Japan
email: help@nag-j.co.jp

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