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.
Fortran 90/95/2003 users are advised that the compiled *.mod files (the interface blocks) have been compiled with the Intel Fortran Compiler 12.1 and are intended for use with that compiler. Users may have to compile the interface blocks themselves if they wish to use them with a different compiler.
When the DLL is used with a non-Intel compiler, please note that two input/output systems are in use: those of Intel for library routines and of course the compiler's own input/output routines for the calling program. This means that programs like the E04UDF example program cannot read the data from just one file. This is because the program reads some of the data using its input/output system. When the option setting routine tries to read the data file, the Intel input/output routines are used. The two input/output systems are completely disjoint and so in particular Intel has no knowledge of the position in the data file that the program input/output system has reached. The problem is circumvented by having two separate data files. Routines affected by this are mainly the option setting routines in chapters H02 and E04.
for details of any new information related to the applicability or usage of this implementation.
In this section we assume that the library has been installed in the default folder:
c:\Program Files\NAG\FS23\fsw3223dclIf 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|FS23|NAG Library for SMP and Multicore (FSW3223DCL) |FSW3223DCL 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.)
To ensure that the NAG DLL is accessible at runtime, the PATH environment variable must be set such that the location of the NAG DLLs, specifically the folder install_dir\bin, is on the path. The install_dir\MKL_ia32_10.3\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 some linear algebra routines (BLAS or LAPACK) are included in FSW3223DC.dll. (See Section 4 for details.)
Start|All Programs|NAG|FS23|NAG Library for SMP and Multicore (FSW3223DCL) |FSW3223DCL Command Promptmay be used to start a command prompt window with the correct settings for the INCLUDE, LIB and PATH environment variables 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\FS23\fsw3223dcl\batch\envvars.batIf the file is not in the default location, you can locate it by searching for the file envvars.bat containing fsw3223dcl.
You may then compile and link to the NAG Library on the command line using one of the following commands:
ifort /iface:cvf /MD /Qopenmp driver.f FSW3223DC_static.lib mkl_rt.lib user32.libwhere driver.f is your application program; or
ifort /iface:cvf /MD /Qopenmp driver.f FSW3223DC.libif the DLL version of the library is required. Note that in the DLL case it is not necessary to explicitly link to the MKL libraries. Notice that in both cases we compile using the /iface:cvf compiler flag. This tells the compiler that we wish to use the CVF calling convention. We also use the /MD compiler flag. This tells the compiler that we wish to link to multi-threaded DLL versions of compiler run-time libraries. Both these flags are important to ensure compatibility with this implementation of the NAG Library for SMP and Multicore. If you do not use them - particularly /iface:cvf - it is likely that your programs will fail to run correctly.
The /Qopenmp flag tells the compiler to heed any OpenMP directives that may be present in your own code. It also causes the linker to link to the compiler threading library, libiomp5md.lib. For older versions of the Intel compiler, a different threading library (named libguide) was used by default. If you are using an older compiler (such as ifort 10.1) then you may need to add libiomp5md.lib explicitly to the compile line, e.g.
ifort /iface:cvf /MD /Qopenmp driver.f FSW3223DC_static.lib mkl_rt.lib user32.lib libiomp5md.libor
ifort /iface:cvf /MD /Qopenmp driver.f FSW3223DC.lib libiomp5md.libto avoid error messages at link or run time.
More information on calling NAG Fortran or C DLLs is available on the NAG web site at
http://www.nag.co.uk/numeric/Num_DLLhelp.aspMore information specific to this product may be available from the Post Release Information page:
To ensure that the NAG DLLs are accessible at runtime, the PATH environment variable must be set such that the location of the NAG DLLs, specifically the folder install_dir\bin, is on the path. The location of the MKL DLLs, install_dir\MKL_ia32_10.3\bin must also be on the path, but should appear after the install_dir\bin folder.
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:
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.
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 the 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/expand 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 FSW3223DC.lib in this location. Alternatively, to link to the static library, add libraries FSW3223DC_static.lib and mkl_rt.lib here. Press the OK button.
You will also need to set the calling convention to "CVF". From the Properties form, click/expand Fortran and then choose External Procedures. Click on the Calling Convention entry in the right hand panel and select CVF from the drop-down list. Selecting this option will automatically change the entry for String Length Argument Passing to After Individual String Argument when you click on Apply or OK; this is the convention required by this implementation of the NAG Library.
We also recommend that you use the multithreaded DLL version of the runtime library. From the Properties form, click/expand Fortran in the leftmost panel and then choose Libraries. Click on the Runtime Library entry in the right hand panel and select Multithread DLL from the drop-down list.
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/expand 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.
As described earlier when compiling from the command line, you may also wish to tell the compiler to use the /Qopenmp switch. From the Properties form, click/expand Fortran in the leftmost panel and then choose Language. Click on the Process OpenMP Directives entry in the right hand panel and select Generate Parallel Code (/QopenMP) from the drop-down list.
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. Select the appropriate settings as detailed in the paragraphs above.
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.
The samples folder of the library installation contains various subfolders which may help if you wish to call the library from C, C++, Microsoft Excel, Microsoft Visual Basic or VB.NET, or the Lahey or gfortran Fortran compilers. We do not give detailed information on how to do that here, but more information may appear on the Post Release Information page:
Otherwise please contact NAG for advice.
set OMP_NUM_THREADS=Nwhere N is the number of threads required. OMP_NUM_THREADS may be re-set between each execution of the program, as desired.
In general, the maximum number of threads you are recommended to use is the number of physical cores on your SMP system.
(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.
The NAG Library for SMP & Multicore interface block files are organised by Library chapter. They are aggregated into one module named
nag_libraryThe modules are supplied in pre-compiled form (.mod files) and they can be accessed by specifying the -module:pathname option on each compiler invocation, where pathname (install_dir\nag_interface_blocks) is the path of the directory containing the compiled interface blocks.
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), and the Intel ifort compiler, 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.
The .mod module files were compiled with the compiler shown in Section 2.1 of the Installer's Note. Such module files are compiler-dependent.
If you wish to use NAG modules with a Fortran compiler other than the Intel compiler, you will need to recompile the interface blocks with your own compiler, as decscribed here.
Copy all the .f90 files from the nag_interface_blocks folder to a new folder of your choice, for example (if you wish to use them with the NAG compiler nagfor) nag_interface_blocks_nagfor. Then compile all the files into objects using your compiler. Because the interface blocks contain some inter-dependencies, the order of compilation is important, but the following compilation order should work (again, using the NAG compiler as an example):
nagfor -f77 -w=x95 -c nag_precisions.f90 nagfor -f77 -w=x95 -c nag_blas_consts.f90 nagfor -f77 -w=x95 -c nag_a_ib.f90 nagfor -f77 -w=x95 -c nag_blas_ib.f90 nagfor -f77 -w=x95 -c nag_blast_ib.f90 nagfor -f77 -w=x95 -c nag_c_ib.f90 nagfor -f77 -w=x95 -c nag_d_ib.f90 nagfor -f77 -w=x95 -c nag_e_ib.f90 nagfor -f77 -w=x95 -c nag_f_ib.f90 nagfor -f77 -w=x95 -c nag_g_ib.f90 nagfor -f77 -w=x95 -c nag_h_ib.f90 nagfor -f77 -w=x95 -c nag_lapack_ib.f90 nagfor -f77 -w=x95 -c nag_m_ib.f90 nagfor -f77 -w=x95 -c nag_p_ib.f90 nagfor -f77 -w=x95 -c nag_s_ib.f90 nagfor -f77 -w=x95 -c nag_x_ib.f90 nagfor -f77 -w=x95 -c nag_long_names.f90 nagfor -f77 -w=x95 -c nag_library.f90(N.B. here the nagfor -f77 flag is used to generate modules with the STDCALL calling convention. The -w=x95 flag suppresses warnings about long symbol names. For other compilers, different flags may be necessary).
To use the newly compiled module files, you will need a compiler-dependent switch to tell the compiler where to find them when you are compiling programs. For example, with the NAG compiler, the command
nagfor -f77 -w=x95 -I nag_interface_blocks_nagforwill tell the compiler to look in the new folder for module files.
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 the batch files nagsmp_example_static.bat or nagsmp_example_dll.bat which are in the folder install_dir\batch.
The batch files need the environment variable NAG_FSW3223DCL.
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_FSW3223DCL. This shortcut is placed in the Start Menu under
Start|All Programs|NAG|FS23|NAG Library for SMP and Multicore (FSW3223DCL) |FSW3223DCL Command PromptIf 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\FS23\fsw3223dcl\batch\envvars.batIf the file is not in the default location, you can locate it by searching for the file envvars.bat containing FSW3223DCL.
The batch script nagsmp_example_static.bat will provide you with a copy of an example program (and its data, if any), compile the program and link it with the library FSW3223DC_static.lib and the MKL. Finally, the executable program will be run.
The example program concerned, and the number of OpenMP threads to use, are specified by the arguments to nagsmp_example_static.bat, e.g.
nagsmp_example_static e04ucf 4will copy the example program e04ucfe.f and its data file e04ucfe.d into the current directory and process them to produce the example program results in the file e04ucfe.r.
Alternatively you could use:
nagsmp_example_dll e04ucf 4
The difference between nagsmp_example_static.bat and nagsmp_example_dll.bat is that while nagsmp_example_static.bat links to the static version of the NAG SMP and MKL Libraries, nagsmp_example_dll.bat links to the DLL versions of the libraries.
REAL(KIND=nag_wp)appears in documentation of all NAG Library for SMP & Multicore routines, where nag_wp is a Fortran KIND parameter. The value of nag_wp will vary between implementations, and its value can be obtained by use of the nag_library module. We refer to the type nag_wp as the NAG Library "working precision" type, because most floating-point arguments and internal variables used in the library are of this type.
In addition, a small number of routines use the type
REAL(KIND=nag_rp)where nag_rp stands for "reduced precision type". Another type, not currently used in the library, is
REAL(KIND=nag_hp)for "higher precision type" or "additional precision type".
For correct use of these types, see almost any of the example programs distributed with the Library.
For this implementation, these types have the following meanings:
REAL (kind=nag_rp) means REAL (i.e. single precision) REAL (kind=nag_wp) means DOUBLE PRECISION COMPLEX (kind=nag_rp) means COMPLEX (i.e. single precision complex) COMPLEX (kind=nag_wp) means double precision complex (e.g. COMPLEX*16)
In addition, the Manual has adopted a convention of using bold italics to distinguish some terms.
One 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
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.
C06PAF C06PCF C06PFF C06PJF C06PKF C06PPF C06PQF C06PRF C06PSF C06PUF C06PXF C06RAF C06RBF C06RCF C06RDFThe Intel DFTI routines allocate their own workspace internally, so no changes are needed to the size of workspace array WORK passed to the NAG C06 routines listed above from that specified in their respective library documents.
In this implementation calls to BLAS and LAPACK routines are implemented by calls to MKL,
except for the following routines:
DGGES DSBEV DSBEVX DSTEDC DTGSNA ZGGES ZGGESX ZHBEV ZHBEVX ZTGSNA
F07ADF/DGETRF F07AEF/DGETRS F07AHF/DGERFS F07ARF/ZGETRF F07ASF/ZGETRS F07AVF/ZGERFS F07BDF/DGBTRF F07BEF/DGBTRS F07BHF/DGBRFS F07BRF/ZGBTRF F07BSF/ZGBTRS F07BVF/ZGBRFS F07CHF/DGTRFS F07CVF/ZGTRFS F07FDF/DPOTRF F07FEF/DPOTRS F07FHF/DPORFS F07FJF/DPOTRI F07FRF/ZPOTRF F07FSF/ZPOTRS F07FVF/ZPORFS F07GEF/DPPTRS F07GHF/DPPRFS F07GSF/ZPPTRS F07GVF/ZPPRFS F07HEF/DPBTRS F07HHF/DPBRFS F07HSF/ZPBTRS F07HVF/ZPBRFS F07JHF/DPTRFS F07JVF/ZPTRFS F07MHF/DSYRFS F07MVF/ZHERFS F07NVF/ZSYRFS F07PHF/DSPRFS F07PVF/ZHPRFS F07QVF/ZSPRFS F07THF/DTRRFS F07TVF/ZTRRFS F07UEF/DTPTRS F07UHF/DTPRFS F07USF/ZTPTRS F07UVF/ZTPRFS F07VEF/DTBTRS F07VHF/DTBRFS F07VSF/ZTBTRS F07VVF/ZTBRFS F08AEF/DGEQRF F08AFF/DORGQR F08AGF/DORMQR F08ASF/ZGEQRF F08ATF/ZUNGQR F08AUF/ZUNMQR F08FEF/DSYTRD F08FFF/DORGTR F08FSF/ZHETRD F08FTF/ZUNGTR F08GFF/DOPGTR F08GTF/ZUPGTR F08HEF/DSBTRD F08HSF/ZHBTRD F08JEF/DSTEQR F08JJF/DSTEBZ F08JKF/DSTEIN F08JSF/ZSTEQR F08JXF/ZSTEIN F08KEF/DGEBRD F08KSF/ZGEBRD F08MEF/DBDSQR F08MSF/ZBDSQR F08NEF/DGEHRD F08NGF/DORMHR F08NSF/ZGEHRD F08PEF/DHSEQR F08PKF/DHSEIN F08PSF/ZHSEQR F08PXF/ZHSEIN F08TAF/DSPGV F08TBF/DSPGVX F08TCF/DSPGVD F08TNF/ZHPGV F08TPF/ZHPGVX F08TQF/ZHPGVD
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 < 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 Im(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 < 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 Re(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
X01AAF (pi) = 3.1415926535897932 X01ABF (gamma) = 0.5772156649015328
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.
The routine X03AAW changes the floating-point control word such that it sets the working precision to double precision (53-bit mantissa) and sets the rounding mode to nearest. X03AAW takes a single INTEGER argument, which is used to store the floating-point control word value on input and return it to the calling program, so this routine is also used to retrieve the original (i.e. on entry) value of the control word.
The routine X03AAX sets the floating-point control word to the value specified in its single INTEGER argument. It is typically used to restore the floating-point control word to its original value after a call to X03AAW, but may, of course, be used to set a different value.
The Library is designed to operate in double precision (53-bit) mode, not the extended precision mode also possible on the chip. A normal Intel Fortran program will operate, by default, in this mode, but other environments may re-set the floating-point control word so that the chip operates in extended precision mode. Excel is one such environment. To obtain consistent behaviour the user may wish to use X03AAW directly before entering any other Library routine in order to restore the mode of operation to double precision.
A corollary of the behaviour of these two routines is that they may also be used as a "get and set" pair, with X03AAW used to get the value of the floating-point control word on entry, and X03AAX used to set a new value (or restore the original value), but note the "side-effect" of calling X03AAW, namely that this will set the control word as described above.
The Library Manual is available as part of the installation or via download from the NAG website. The most up-to-date version of the documentation is accessible via the NAG website at http://www.nag.co.uk/numeric/FL/FSdocumentation.asp.
The Library Manual is supplied in the following formats:
The following main index files have been provided for these formats:
nagdoc_fl23\xhtml\FRONTMATTER\manconts.xml nagdoc_fl23\pdf\FRONTMATTER\manconts.pdf nagdoc_fl23\html\FRONTMATTER\manconts.htmlUse your web browser to navigate from here. For convenience, a master index file containing links to the above files has been provided at
Advice on viewing and navigating the formats available can be found in the Online Documentation document.
In addition the following are provided:
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 or account number and NAG product code (in this case FSW3223DCL).
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:
NAG Ltd Wilkinson House Jordan Hill Road OXFORD OX2 8DR NAG Ltd Response Centre United Kingdom email: email@example.com Tel: +44 (0)1865 511245 Tel: +44 (0)1865 311744 Fax: +44 (0)1865 310139 Fax: +44 (0)1865 310139 NAG Inc 801 Warrenville Road Suite 185 Lisle, IL 60532-4332 NAG Inc Response Center USA email: firstname.lastname@example.org Tel: +1 630 971 2337 Tel: +1 630 971 2337 Fax: +1 630 971 2706 Fax: +1 630 971 2706 Nihon NAG KK Hatchobori Frontier Building 2F 4-9-9 Hatchobori Chuo-ku Tokyo 104-0032 Nihon NAG Response Centre Japan email: email@example.com Tel: +81 3 5542 6311 Tel: +81 3 5542 6311 Fax: +81 3 5542 6312 Fax: +81 3 5542 6312 NAG Taiwan Branch Office 5F.-5, No.36, Sec.3 Minsheng E. Rd. Taipei City 10480 NAG Taiwan Response Centre Taiwan email: firstname.lastname@example.org Tel: +886 2 25093288 Tel: +886 2 25093288 Fax: +886 2 25091798 Fax: +886 2 25091798