NAG C Library, Mark 24

CLW3224DAL - License Managed

Microsoft Windows XP / Vista / 7 / 8, 32-bit, Intel C/C++ or Microsoft C/C++

Users' Note



Contents


1. Introduction

This document is essential reading for every user of the NAG C Library implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Mark 24 C 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/cl24/w32dal/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 use one of the variants of the NAG C Library which is based on the supplied Intel ® Math Kernel Library (MKL) i.e. nagc_mkl_MT.lib, nagc_mkl_MD.lib or CLW3224DA_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 nagc_nag_MT.lib, nagc_nag_MD.lib or CLW3224DA_nag.dll.

Which static variant of the NAG Library you should use will also depend on how you wish to link to the Microsoft run-time libraries. For example, if you are linking with the multithreaded static run-time libraries, you should use nagc_mkl_MT.lib or nagc_nag_MT.lib, whereas if you are linking with the multithreaded dynamic link run-time libraries, you should use nagc_mkl_MD.lib or nagc_nag_MD.lib. Alternatively, if you wish to call a dynamic link library (DLL) variant of the NAG Library, you should link with the import library CLW3224DA_mkl.lib or CLW3224DA_nag.lib (and, at run time, make sure that the corresponding DLL, CLW3224DA_mkl.dll or CLW3224DA_nag.dll, is on your path). For more details, see Section 3.1.1.

Note that the NAG C Library is carefully designed so that any memory used can be reclaimed - either by the Library itself or by the user invoking calls of NAG_FREE(). However, the Library does itself depend on the use of compiler run-time and other libraries which may sometimes leak memory, and memory tracing tools used on programs linked to the NAG Library may report this. The amount of memory leaked will vary from application to application, but should not be excessive and should never increase without limit as more calls are made to the NAG Library.

If your machine has more than one processor or core, then it is recommended that you set the environment variable OMP_NUM_THREADS to the number of available cores, e.g.

  set OMP_NUM_THREADS=4
This will enable the Intel MKL BLAS to make use of the extra processor(s) and will thus speed up the computation of many of the Library procedures.

With MKL version 10.0 or newer, this is the default behaviour. In this case, if you do not want MKL to make use of multiple cores, OMP_NUM_THREADS must be set to 1.

If you are running on an Intel processor and using an MKL-based variant of the NAG Library, performance may be enhanced by using the Conditional Numerical Reproducibility settings introduced in MKL 11.0. To get the best performance from the MKL routines, set the environment variable MKL_CBWR appropriately for your processor. See http://software.intel.com/sites/products/documentation/doclib/mkl_sa/11/mkl_userguide_win/index.htm#GUID-DCB010F6-DDBF-4A00-8BB3-049BEFDC2ED2.htm for the various settings available. Alternatively, call the mkl_set_cbwr_branch function from your code prior to calling any NAG Library routines.

3.1. Accessing the Library

In this section we assume that the Library and the NAG include files have been installed under the default folder:
  C:\Program Files\NAG\CL24\clw3224dal
or (if you are installing this 32-bit library on a 64-bit machine)
  C:\Program Files (x86)\NAG\CL24\clw3224dal
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|CL24|NAG C Library (CLW3224DAL)|
      NAG CLW3224DAL Command Prompt
If this shortcut does not exist, please consult the system manager (or the person who did the installation). (Other shortcuts created as part of the Library installation procedure are also assumed to be in this location.)

(Under Windows 8, the shortcuts appear under the list of all applications. To find this, right-click on the background of the Start screen and click on the All apps button, which is typically located near the bottom left or bottom right corner of the screen. The shortcuts are listed under the NAG section.)

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 (CLW3224DA_mkl.dll or CLW3224DA_nag.dll) is accessible at run time; therefore the install dir\bin folder must be on the path. The install dir\rtl\bin folder must be on the path too (unless you have the appropriate Intel run-time libraries on your path already). If an MKL-based version of the Library is to be used, the install dir\mkl_ia32_11.1\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 Basic Linear Algebra Subprograms (BLAS) / Linear Algebra PACKage (LAPACK) routines are included in the NAG Libraries to avoid problems with the vendor versions. (See Section 4 for details.)

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

  Start|All Programs|NAG|CL24|NAG C Library (CLW3224DAL)|
      Check NAG DLL Accessibility for CLW3224DAL
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|CL24|NAG C Library (CLW3224DAL)|
      NAG CLW3224DAL 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 supplied MKL. The environment variable NAG_CLW3224DAL, which is needed by the nagc_example_*.bat batch files is also set.

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 for this file is:

  C:\Program Files\NAG\CL24\clw3224dal\batch\envvars.bat
If this file is not in the default location, you can locate it by searching for the file envvars.bat containing clw3224dal.

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

  cl /MD driver.c CLW3224DA_mkl.lib

  cl /MD driver.c CLW3224DA_nag.lib

  cl /MT driver.c nagc_mkl_MT.lib mkl_intel_s.lib mkl_intel_thread.lib
      mkl_core.lib libiomp5md.lib user32.lib advapi32.lib

  cl /MT driver.c nagc_nag_MT.lib user32.lib advapi32.lib

  cl /MD driver.c nagc_mkl_MD.lib mkl_intel_s.lib mkl_intel_thread.lib
      mkl_core.lib libiomp5md.lib user32.lib advapi32.lib

  cl /MD driver.c nagc_nag_MD.lib user32.lib advapi32.lib
where driver.c is your application program. (Note - this assumes use of the Microsoft C compiler cl. You may also use the Intel C compiler icl. Options for both compilers are the same.)

The C/C++ compiler options:

/MD
means compile code to link with the import library for the multithreaded DLL version of the C run-time library
/MT
means compile code to link with the static multithreaded version of the C run-time library
These options should be used consistently throughout your project.

CLW3224DA_mkl.lib is a DLL import library that makes use of MKL for BLAS/LAPACK routines. CLW3224DA_nag.lib is a DLL import library that includes NAG BLAS/LAPACK. Both libraries have been compiled with the /MD option. This option must be used when compiling applications to be linked with either of these libraries to ensure linking to the correct C run-time libraries.

nagc_mkl_MT.lib is a static library that does not include BLAS/LAPACK and should be linked to the MKL static libraries. nagc_nag_MT.lib is a static library that includes NAG BLAS/LAPACK. Both libraries have been compiled with the /MT option. This option must be used when compiling applications to be linked with either of these libraries to ensure linking to the correct C run-time libraries.

nagc_mkl_MD.lib is a static library that does not include BLAS/LAPACK and should be linked to the MKL static libraries. nagc_nag_MD.lib is a static library that includes NAG BLAS/LAPACK. Both libraries have been compiled with the /MD option. This option must be used when compiling applications to be linked with either of these libraries to ensure linking to the correct C run-time libraries.

More information on calling NAG DLLs is available on the NAG web site at http://www.nag.co.uk/numeric/Num_DLLhelp.asp

More information specific to this product may be available from the Post Release Information page:

http://www.nag.co.uk/doc/inun/cl24/w32dal/postrelease.html

3.1.2. From MS Visual Studio

The following instructions apply to Microsoft Visual Studio 2012. If a different version of Visual Studio is being used the procedure may differ slightly.

If it is planned to use Microsoft Visual Studio to build programs that use the NAG C Library, each user should set the appropriate options.

Start Visual Studio and create your project in the usual way. We assume that your project is going to make use of the NAG C Library.

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.

The following steps show how to add the NAG Library to the project:

  1. Open the Property Pages for the project. There are several ways of doing this including:

  2. From the form, click/expand Configuration Properties and then VC++ Directories in the leftmost panel. Then

    The default folders are as follows:

      Include Directories
        "C:\Program Files\NAG\CL24\clw3224dal\include"
      Library Directories
        "C:\Program Files\NAG\CL24\clw3224dal\lib"
        "C:\Program Files\NAG\CL24\clw3224dal\rtl\lib"
        "C:\Program Files\NAG\CL24\clw3224dal\mkl_ia32_11.1\lib"
    
    Click on the Apply button to accept the changes.

  3. The NAG C Library and Intel run-time libraries (and possibly the MKL libraries) need to be specified in the linker options. From the Property Pages form, click/expand Linker in the leftmost panel (also under Configuration Properties) and then choose Input. Add the appropriate library files to the Additional Dependencies list; please see the table below.

    In addition, you may need to add the flag /SAFESEH:NO to the avoid linker errors. Within the Linker section, click/expand Command Line and add /SAFESEH:NO under Additional Options to add this to the linker command line.

    Click on the OK button to accept the changes and close the form.

  4. Additionally the appropriate C run-time library option needs to be set. First add your C file, e.g. a NAG example program, to the project, using Add Existing Item... from the Project menu. (If you don't have a C file in the project, the C++ options may not be visible.)

    Open the Property Pages again (as detailed above) and click/expand Configuration Properties (if required) and then C/C++, then click on Code Generation in the left hand panel. Then, from the right hand panel, select Runtime Library and change this to the appropriate version, for example /MD or /MT. This must match the version of the NAG C Library that you link to.

    Click on the OK button to accept the changes and close the form.

NAG C Library MKL and other Libraries C Run-time Libraries
CLW3224DA_mkl.lib (Not required at link time) Multi-threaded DLL (/MD)
CLW3224DA_nag.lib   Multi-threaded DLL (/MD)
nagc_mkl_MT.lib mkl_intel_s.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib Multi-threaded (/MT)
nagc_nag_MT.lib   Multi-threaded (/MT)
nagc_mkl_MD.lib mkl_intel_s.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib Multi-threaded DLL (/MD)
nagc_nag_MD.lib   Multi-threaded DLL (/MD)

If you are running on a 64-bit system, make sure the Platform is set to Win32 (to ensure compatibility with this 32-bit implementation of the NAG Library). This can be changed via the Configuration Manager... button on the Property Pages.

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

To run a program from within the Microsoft Development Environment, the program may be executed via the Debug menu (by selecting Start Without Debugging, for example). Note that the PATH environment variable must be set appropriately, as detailed in Section 3.1 above.

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, this can be achieved by selecting the Debugging section on the Properties form and inserting the appropriate commands in the Command Arguments field, e.g.

  < input_file > output_file
If the input and output files are not in the application's working directory, full or relative paths may need to be specified. For NAG examples that use an .opt file, this should be placed in the working directory. This directory may be set via the Working Directory field, which is also on the Debugging page of the Properties form. (Note that input / output redirection is broken in some versions of Visual Studio 2008.)

3.2. Example Programs

The example results distributed were generated at Mark 24, 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 C 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.

The distributed example results are those obtained with the MKL-based DLL library CLW3224DA_mkl.dll (using the MKL BLAS and LAPACK routines). Running the examples with NAG BLAS or LAPACK may give slightly different results.

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 using the batch files nagc_example_dll.bat, nagc_example_static_MT.bat and nagc_example_static_MD.bat, which can be found in the install dir\batch folder. These batch files 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, with the results being sent to a file and to the command window.

These batch files require that the environment variables for your C/C++ compiler and the NAG C Library are set. In particular, the environment variable NAG_CLW3224DAL needs to be set to the location of the NAG C Library. Please see Section 3.1.1 for details of how to do this.

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

  nagc_example_dll e04ucc
will copy the example program, data and options files e04ucce.c, e04ucce.d and e04ucce.opt into the current directory and process them to produce the example program results in the file e04ucce.r.

nagc_example_dll.bat links to the DLL version of the NAG C library using NAG BLAS/LAPACK.

To link with the MKL version of the DLL, use the -mkl option, e.g.

  nagc_example_dll -mkl e04ucc

The nagc_example_static_MD batch file is used in the same way and links to the static NAG C Library compiled with /MD.

  nagc_example_static_MT e04ucc
Again, it is possible to link the MKL BLAS/LAPACK by using the -mkl option
  nagc_example_static_MD -mkl e04ucc

The nagc_example_static_MT.bat batch file links to the static library using NAG BLAS/LAPACK compiled with /MT, e.g.

  nagc_example_static_MT e04ucc
  nagc_example_static_MT -mkl e04ucc
The first command links with the static library using NAG BLAS/LAPACK. To link with the MKL version of the library, use the -mkl option, as shown in the second command.

3.3. Data Types

In this implementation, the NAG types Integer and Pointer are defined as follows:
 NAG Type   C Type   Size (bytes) 
 Integer   int     4 
 Pointer   void *   4 

The values for sizeof(Integer) and sizeof(Pointer) are also given by the a00aac example program. Information on other NAG data types is available in the Essential Introduction section of the Library Manual (see Section 5).

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, f08 and f16

    In this implementation calls to the NAG version of the following BLAS and LAPACK routines are included in the libraries nagc_mkl_MD.lib, nagc_mkl_MT.lib and CLW3224DA_mkl.dll to avoid problems with the vendor version:
       dgees     dgeesx   dgemqrt   dgeqrt   dgges
       dggesx    dsbev    dsbevx    dstedc   dstevr
       dtgsna    dtpmqrt  dtpqrt    zgees    zgeesx
       zgemqrt   zgeqrt   zgges     zggesx   zhbev
       zhbevx    ztgsna   ztpmqrt   ztpqrt   ztrsen
    
  2. s10 - s21

    The behaviour of functions in these Chapters may depend on implementation-specific values.

    General details are given in the Library Manual, but the specific values used in this implementation are as follows:

    s10aac  E_1 = 1.8715e+1
    s10abc  E_1 = 7.080e+2
    s10acc  E_1 = 7.080e+2
    
    s13aac  x_hi = 7.083e+2
    s13acc  x_hi = 1.0e+16
    s13adc  x_hi = 1.0e+17
    
    s14aac  fail.code = NE_REAL_ARG_GT if x > 1.70e+2
            fail.code = NE_REAL_ARG_LT if x < -1.70e+2
            fail.code = NE_REAL_ARG_TOO_SMALL if abs(x) < 2.23e-308
    s14abc  fail.code = NE_REAL_ARG_GT if x > x_big = 2.55e+305
    
    s15adc  x_hi = 2.65e+1
    s15aec  x_hi = 2.65e+1
    s15agc  fail.code = NW_HI if x >= 2.53e+307
            fail.code = NW_REAL if 4.74e+7 <= x < 2.53e+307
            fail.code = NW_NEG if x < -2.66e+1
    
    s17acc  fail.code = NE_REAL_ARG_GT if x > 1.0e+16
    s17adc  fail.code = NE_REAL_ARG_GT if x > 1.0e+16
            fail.code = NE_REAL_ARG_TOO_SMALL if 0 < x <= 2.23e-308
    s17aec  fail.code = NE_REAL_ARG_GT if abs(x) > 1.0e+16
    s17afc  fail.code = NE_REAL_ARG_GT if abs(x) > 1.0e+16
    s17agc  fail.code = NE_REAL_ARG_GT if x > 1.038e+2
            fail.code = NE_REAL_ARG_LT if x < -5.7e+10
    s17ahc  fail.code = NE_REAL_ARG_GT if x > 1.041e+2
            fail.code = NE_REAL_ARG_LT if x < -5.7e+10
    s17ajc  fail.code = NE_REAL_ARG_GT if x > 1.041e+2
            fail.code = NE_REAL_ARG_LT if x < -1.9e+9
    s17akc  fail.code = NE_REAL_ARG_GT if x > 1.041e+2
            fail.code = NE_REAL_ARG_LT if x < -1.9e+9
    s17dcc  fail.code = NE_OVERFLOW_LIKELY if abs(z) < 3.92223e-305
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    s17dec  fail.code = NE_OVERFLOW_LIKELY if AIMAG(z) > 7.00921e+2
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    s17dgc  fail.code = NW_SOME_PRECISION_LOSS if abs(z) > 1.02399e+3
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) > 1.04857e+6
    s17dhc  fail.code = NW_SOME_PRECISION_LOSS if abs(z) > 1.02399e+3
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) > 1.04857e+6
    s17dlc  fail.code = NE_OVERFLOW_LIKELY if abs(z) < 3.92223e-305
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    
    s18adc  fail.code = NE_REAL_ARG_TOO_SMALL if 0 < x <= 2.23e-308
    s18aec  fail.code = NE_REAL_ARG_GT if abs(x) > 7.116e+2
    s18afc  fail.code = NE_REAL_ARG_GT if abs(x) > 7.116e+2
    s18dcc  fail.code = NE_OVERFLOW_LIKELY if abs(z) < 3.92223e-305
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    s18dec  fail.code = NE_OVERFLOW_LIKELY if REAL(z) > 7.00921e+2
            fail.code = NW_SOME_PRECISION_LOSS if abs(z) or fnu+n-1 > 3.27679e+4
            fail.code = NE_TOTAL_PRECISION_LOSS if abs(z) or fnu+n-1 > 1.07374e+9
    
    s19aac  fail.code = NE_REAL_ARG_GT if abs(x) >= 5.04818e+1
    s19abc  fail.code = NE_REAL_ARG_GT if abs(x) >= 5.04818e+1
    s19acc  fail.code = NE_REAL_ARG_GT if x > 9.9726e+2
    s19adc  fail.code = NE_REAL_ARG_GT if x > 9.9726e+2
    
    s21bcc  fail.code = NE_REAL_ARG_LT if an argument < 1.583e-205
            fail.code = NE_REAL_ARG_GE if an argument >= 3.765e+202
    s21bdc  fail.code = NE_REAL_ARG_LT if an argument < 2.813e-103
            fail.code = NE_REAL_ARG_GT if an argument >= 1.407e+102
    
  3. x01

    The values of the mathematical constants are provided in the header file nagx01.h:

    X01AAC (pi) = 3.1415926535897932
    X01ABC (gamma) = 0.5772156649015328
    
  4. x02

    The values of the machine constants are provided in the header file nagx02.h:

    The basic parameters of the model

    X02BHC   = 2
    X02BJC   = 53
    X02BKC   = -1021
    X02BLC   = 1024
    

    Derived parameters of the floating-point arithmetic

    X02AJC   = 1.11022302462516e-16
    X02AKC   = 2.22507385850721e-308
    X02ALC   = 1.79769313486231e+308
    X02AMC   = 2.22507385850721e-308
    X02ANC   = 2.22507385850721e-308
    

    Parameters of other aspects of the computing environment

    X02AHC   = 1.42724769270596e+45
    X02BBC   = 2147483647
    X02BEC   = 15
    

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. The most up-to-date version of the documentation is accessible via the NAG website at http://www.nag.co.uk/numeric/CL/CLdocumentation.asp.

The Library Manual is supplied in the following formats:

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

	nagdoc_cl24/html/FRONTMATTER/manconts.html
	nagdoc_cl24/pdf/FRONTMATTER/manconts.pdf
	nagdoc_cl24/pdf/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|Mark 24 Manual|
      NAG C Library Manual Mark 24 (HTML5)
  Start|All Programs|NAG|Mark 24 Manual|
      NAG C Library Manual Mark 24 (PDF)
  Start|All Programs|NAG|Mark 24 Manual|
      NAG C Library Manual Mark 24 (PDF + HTML Index)
respectively, by default. Use your web browser to navigate from here. For convenience, a master index file containing links to the above files has been provided at
	nagdoc_cl24/index.html

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

The Library Manual is also available as an HTML Help file. The HTML Help version of the Library Manual is available from the Start Menu under

  Start|All Programs|NAG|CL24|NAG C Library (CLW3224DAL)|
      NAG C Library Manual Mk24 HTML Help
If the NAG Library materials have been installed on a network drive, you may need to copy the HTML Help file (nagdoc_cl24.chm) to a local drive. If you still have trouble seeing the correct help file materials, e.g. if you see a message such as
  Navigation to the webpage was canceled
the file might have been blocked by security updates in Windows or Internet Explorer. Right-click on nagdoc_cl24.chm in Windows Explorer and select Properties from the pop-up menu. If there is an Unblock button at the bottom click on it to unblock the file and then click on OK to close the Properties dialog box.

In addition the following are provided:

The latter is available from the Start Menu under
  Start|All Programs|NAG|CL24|NAG C Library (CLW3224DAL)|
      NAG CLW3224DAL 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 our support team (see below).

(b) NAG Technical Support Service

The NAG Technical Support Service is available for general enquiries from all users and also for technical queries from sites with an annually licensed product or support service.

The technical support desks are open during office hours, but contact is possible by email and phone (answering machine) at all times.

When contacting us, it helps us deal with your enquiry quickly if you can quote your NAG customer reference number and NAG product code (in this case CLW3224DAL).

(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 offices (shown below).

Appendix - Contact Addresses

NAG Ltd
Wilkinson House
Jordan Hill Road
OXFORD  OX2 8DR                         Technical Support (Europe & ROW)
United Kingdom                          email: support@nag.co.uk

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

NAG Inc
801 Warrenville Road
Suite 185
Lisle, IL  60532-4332                   Technical Support (North America)
USA                                     email: support@nag.com

Tel: +1 630 971 2337                    Tel: +1 630 971 2337

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

Tel: +81 3 5542 6311                    Tel: +81 3 5542 6311