In addition, NAG recommends that before calling any Library routine you should read the following reference material from the Library Manual (see Section 5):
(a) How to Use the NAG Library and its Documentation
(b) Chapter Introduction
(c) Routine Document
for details of any new information related to the applicability or usage of this implementation.
This implementation of the NAG Library provides static and shared libraries that use a third-party vendor performance library to provide Basic Linear Algebra Subprograms (BLAS) and Linear Algebra PACKage (LAPACK) routines (see below). It also provides static and shared libraries that use the NAG versions of these routines (referred to as the self-contained libraries).
This implementation of the NAG Library has been tested with version 2017.0.3 of the Intel ® Math Kernel Library for Windows (MKL) which is supplied as a part of this product. Please see the Intel website for further information about MKL (https://software.intel.com/intel-mkl).
For best performance, we recommend that you use one of the variants of the NAG Library which is based on the supplied MKL, i.e. nagc_mkl_MT.lib, nagc_mkl_MD.lib or CLW6I261E_mkl.lib/CLW6I261E_mkl.dll. These libraries do not contain the NAG versions of the BLAS and LAPACK routines (except for any routines listed in Section 4(a)).
The self-contained libraries, nagc_nag_MT.lib, nagc_nag_MD.lib and CLW6I261E_nag.lib/CLW6I261E_nag.dll, are also supplied. These contain the NAG versions of the BLAS and LAPACK routines.
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 CLW6I261E_mkl.lib or CLW6I261E_nag.lib (and, at run time, make sure that the corresponding DLL, CLW6I261E_mkl.dll or CLW6I261E_nag.dll is on your path). For more details, see Section 3.1.1.
Note that the NAG 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.
The version of Intel MKL supplied is multithreaded. If the environment variable OMP_NUM_THREADS is undefined, MKL may create multiple threads to speed up computation on systems with more than one processor or a multicore chip. If you do not want MKL to make use of multiple cores or processors, OMP_NUM_THREADS must be set to 1.
Alternatively, set the environment variable to the number of threads required. Note that the Chapter X06 routines do not change the behaviour of MKL threading in serial implementations of the Library.
Intel have introduced a conditional bitwise reproducibility (BWR) option in MKL. Provided a user's code adheres to certain conditions (see https://software.intel.com/en-us/node/528579), BWR can be forced by setting the MKL_CBWR environment variable. See the MKL documentation for further details. It should be noted, however, that many NAG routines do not adhere to these conditions. This means that for a given NAG library built on top of MKL, it may not be possible to ensure BWR for all NAG routines across different CPU architectures by setting MKL_CBWR. See Section 3.9.1 of How to Use the NAG Library and its Documentation for more general information on bitwise reproducibility.
In this section we assume that the Library has been installed in the default folder, namely
C:\Program Files\NAG\CL26\clw6i261elThe actual name of the "Program Files" folder may appear differently, depending on your locale. If the above 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 shortcut for the Library command prompt is in the NAG C Library (CLW6I261EL) section of the Start Menu or All apps under:
NAG CLW6I261EL Command PromptIf 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.)
If you are using a DLL form of the Library (see Section 3.1.1), you need to ensure that the NAG DLL (CLW6I261E_mkl.dll or CLW6I261E_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_intel64_2017.0.3\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 a few BLAS / LAPACK routines may be included in the NAG Libraries to avoid problems with the vendor versions. (See Section 4 for details.)
To check the accessibility of the NAG DLLs, run the program NAG_C_DLL_info.exe which is available from the Start Menu or All apps shortcut
Check NAG CLW6I261EL DLL AccessibilitySee Section 4.2.2 of the Installer's Note for details of this utility.
NAG CLW6I261EL Command Promptmay 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. The environment variable NAG_CLW6I261EL, 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\CL26\clw6i261el\batch\envvars.batIf this file is not in the default location, you can locate it by searching for the file envvars.bat containing clw6i261el.
You may then compile and link to the NAG Library on the command line using one of the following commands:
cl /MD driver.c CLW6I261E_mkl.lib cl /MD driver.c CLW6I261E_nag.lib cl /MT driver.c nagc_mkl_MT.lib mkl_intel_lp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib cl /MT driver.c nagc_nag_MT.lib user32.lib cl /MD driver.c nagc_mkl_MD.lib mkl_intel_lp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib cl /MD driver.c nagc_nag_MD.lib user32.libwhere driver.c is your application program. (Note – we assume above use of the Microsoft C compiler cl. You may also use the Intel C compiler icl. Options for both compilers are the same.)
The compiler options:
CLW6I261E_mkl.lib is a DLL import library that makes use of MKL for BLAS/LAPACK routines. CLW6I261E_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 such 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 such 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 such libraries to ensure linking to the correct C run-time libraries.
If it is planned to use Microsoft Visual Studio to build programs that use the NAG 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 Library.
The library is intended to be run in fully optimized mode, so to avoid any warning messages, you might decide to set the active configuration to Release. Once Visual Studio has been opened, 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 run-time libraries.
Make sure the Platform is set to x64 (to ensure compatibility with this 64-bit implementation of the NAG Library). This can be changed via the Configuration Manager... button on the Property Pages.
The following steps show how to add the NAG Library to the project:
The default folders are as follows:
Include Directories C:\Program Files\NAG\CL26\clw6i261el\include Library Directories C:\Program Files\NAG\CL26\clw6i261el\lib C:\Program Files\NAG\CL26\clw6i261el\rtl\lib C:\Program Files\NAG\CL26\clw6i261el\mkl_intel64_2017.0.3\libClick on the Apply button to accept the changes.
Click on the OK button to accept the changes and close the form.
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 Library that you link to.
Click on the OK button to accept the changes and close the form.
|NAG Library||MKL and other Libraries||C Run-time Libraries|
|CLW6I261E_mkl.lib||(Not required at link time)||Multi-threaded DLL (/MD)|
|CLW6I261E_nag.lib||Multi-threaded DLL (/MD)|
|nagc_mkl_MT.lib||mkl_intel_lp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib||Multi-threaded (/MT)|
|nagc_mkl_MD.lib||mkl_intel_lp64.lib mkl_intel_thread.lib mkl_core.lib libiomp5md.lib user32.lib||Multi-threaded DLL (/MD)|
|nagc_nag_MD.lib||user32.lib||Multi-threaded DLL (/MD)|
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 (Ctrl+F5), 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_fileIf 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.
The distributed example results are those obtained with the static library nagc_mkl_MD.lib (i.e. 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 require that the environment variables for your C/C++ compiler and the NAG Library are set. In particular, the environment variable NAG_CLW6I261EL needs to be set to the location of the NAG Library. Please see Section 3.1.1 for details of how to do this.
Each of the nagc_example_*.bat batch files mentioned above will provide you with a copy of an example program (and its data and options file, 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 appropriate arguments specifying data, options and results files as needed), with the results being sent to a file and to the command window.
The example program concerned is specified by the argument to the command, e.g.
nagc_example_DLL e04uccwill copy the example program and its data and options files (e04ucce.c, e04ucce.d and e04ucce.opt) into the current folder, compile and link the program and run it to produce the example program results in the file e04ucce.r.
nagc_example_DLL.bat links to the DLL version of the NAG 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.bat batch file is used in the same way and links to the static NAG library compiled with /MD.
nagc_example_static_MD e04uccAgain, 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 compiled with /MT, e.g.
nagc_example_static_MT e04ucc nagc_example_static_MT -mkl e04ucc
|NAG Type||C Type||Size (bytes)|
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 How to Use the NAG Library and its Documentation section of the Library Manual (see Section 5).
Alternatively, run the diagnostic program NAG_C_DLL_info.exe which itself calls a00aac (see Installer's Note, Section 4.2.2).
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 CLW6I261E_mkl.dll to avoid problems with the vendor version:
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
The values of the mathematical constants are provided in the header file nagx01.h:
X01AAC (pi) = 3.1415926535897932 X01ABC (gamma) = 0.5772156649015328
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
The Library Manual is available as a separate installation, 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/content/nag-c-library-manual.
The Library Manual is supplied in the following formats:
The following main index files have been provided for these formats:
nagdoc_cl26\html\frontmatter\manconts.html nagdoc_cl26\pdf\frontmatter\manconts.pdf nagdoc_cl26\pdf\frontmatter\manconts.htmlIf the Library Manual has been installed locally, these index files are available from the NAG Mark 26-1 Manual section of the Start Menu or All apps under
NAG C Library Manual Mark 26 (HTML5) NAG C Library Manual Mark 26 (PDF) NAG C Library Manual Mark 26 (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
Advice on viewing and navigating the formats available can be found in http://www.nag.co.uk/numeric/cl/nagdoc_cl26.1/html/ genint/essint.html#onlinedoc.
In addition the following are provided:
NAG CLW6I261EL Users' Noteby default.
for information about the NAG Technical Support Service, including details of the NAG Technical Support Service contact points. We would also be delighted to receive your feedback on NAG's products and services.
for worldwide contact details for the Numerical Algorithms Group.