NAG C Library, Mark 26

CLL6I26DDL - License Managed

Linux 64 (Intel 64 / AMD64), Intel C/C++, 64-bit integers

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 26 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 from the Library Manual (see Section 5):

(a) How to Use the NAG Library and its Documentation
(b) Chapter Introduction
(c) Routine Document

2. Supplementary Information

Please check the following URL:

http://www.nag.co.uk/doc/inun/cl26/l6iddl/supplementary.html

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

3. General Information

This implementation of the NAG C Library provides static and shareable libraries that use the Intel ® Math Kernel Library for Linux (MKL), a third-party vendor performance library, to provide Basic Linear Algebra Subprograms (BLAS) and Linear Algebra PACKage (LAPACK) routines (except for any routines listed in Section 4(a)). It also provides static and shareable libraries that use the NAG versions of these routines (referred to as the self-contained libraries). This implementation has been tested with version 11.3.3 of 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 C Library which is based on the supplied MKL, i.e. libnagc_mkl.a or libnagc_mkl.so, in preference to using one of the self-contained NAG libraries, libnagc_nag.a or libnagc_nag.so.

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.

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, e.g.

  setenv OMP_NUM_THREADS 1
in the C shell, or
  OMP_NUM_THREADS=1
  export OMP_NUM_THREADS
in the Bourne shell.

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.

Please note that this implementation is not compatible with versions of MKL earlier than 10.3.

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 2.9.1 of How to Use the NAG Library and its Documentation for more general information on bitwise reproducibility.

3.1. Accessing the Library

In this section we assume that the Library and the NAG include files have been installed in the directory [INSTALL_DIR].

By default [INSTALL_DIR] (see Installer's Note (in.html)) is $HOME/NAG/cll6i26ddl; however it could have been changed by the person who did the installation, in which case you should consult that person.

To use the NAG C Library and the supplied MKL libraries, you may link in the following manner:


 icc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.a \
   -Wl,--start-group \
   [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_intel_ilp64.a \
   [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_intel_thread.a \
   [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_core.a \
   -Wl,--end-group \
   [INSTALL_DIR]/rtl/intel64/libiomp5.a [INSTALL_DIR]/rtl/intel64/libifcoremt.a \
   -lpthread -lm -ldl -lstdc++
where driver.c is your application program;

or


  icc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.so \
    -L[INSTALL_DIR]/mkl_intel64_11.3.3/lib -lmkl_intel_ilp64 \
    -lmkl_intel_thread -lmkl_core \
    -L[INSTALL_DIR]/rtl/intel64 \
    -liomp5 -lpthread -lm -ldl [INSTALL_DIR]/rtl/intel64/libifcoremt.so
if the shareable library is required. Please note that the shareable library is fully resolved so that you need not link against other run-time libraries (e.g. libmkl_rt.so) explicitly; this requires the environment variable LD_LIBRARY_PATH to be set correctly at link time (see below).

However, if you prefer to link to a version of the NAG C Library which does not require the use of MKL you may wish to use the self-contained libraries as follows:


  icc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.a \
      [INSTALL_DIR]/rtl/intel64/libifcoremt.a -lpthread -lstdc++
or

  icc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.so \
      [INSTALL_DIR]/rtl/intel64/libifcoremt.so -lpthread
if the shareable library is required.

If you want to use a different compiler or indeed a different version of the Intel compiler, icc, you may need to link against the libraries provided in [INSTALL_DIR]/rtl/. For instance, to use gcc, you can use one of the following commands:

To use the MKL-based NAG Library with static linkage:

  gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.a \
    -Wl,--start-group \
    [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_intel_ilp64.a \
    [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_intel_thread.a \
    [INSTALL_DIR]/mkl_intel64_11.3.3/lib/libmkl_core.a \
    -Wl,--end-group \
    [INSTALL_DIR]/rtl/intel64/libiomp5.a \
    [INSTALL_DIR]/rtl/intel64/libifcoremt.a \
    [INSTALL_DIR]/rtl/intel64/libimf.a \
    [INSTALL_DIR]/rtl/intel64/libirc.a \
    [INSTALL_DIR]/rtl/intel64/libsvml.a \
    -lstdc++ -ldl -lpthread -lm
To use the MKL-based NAG Library with shared linkage:
  gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_mkl.so \
    -L[INSTALL_DIR]/mkl_intel64_11.3.3/lib \
    -lmkl_intel_ilp64 -lmkl_intel_thread -lmkl_core \
    -L[INSTALL_DIR]/rtl/intel64 \
    -liomp5 -lifcoremt -limf -lsvml -lintlc -lirng -lstdc++ -lpthread -lm
To use the self-contained NAG Library with static linkage:
  gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.a \
    [INSTALL_DIR]/rtl/intel64/libifcoremt.a [INSTALL_DIR]/rtl/intel64/libimf.a \
    [INSTALL_DIR]/rtl/intel64/libirc.a [INSTALL_DIR]/rtl/intel64/libsvml.a \
    -lstdc++ -ldl -lpthread -lm
To use the self-contained NAG Library with shared linkage:
  gcc driver.c -I[INSTALL_DIR]/include [INSTALL_DIR]/lib/libnagc_nag.so \
     -lstdc++ -lpthread -lm

If your application has been linked with the shareable NAG and MKL libraries then the environment variable LD_LIBRARY_PATH must be set (or extended) to allow run-time linkage.

In the C shell type:


  setenv LD_LIBRARY_PATH [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib
to set LD_LIBRARY_PATH, or

  setenv LD_LIBRARY_PATH \
      [INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib:${LD_LIBRARY_PATH}
to extend LD_LIBRARY_PATH if you already have it set.

In the Bourne shell, type:


  LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib
  export LD_LIBRARY_PATH
to set LD_LIBRARY_PATH, or

  LD_LIBRARY_PATH=[INSTALL_DIR]/lib:[INSTALL_DIR]/mkl_intel64_11.3.3/lib:${LD_LIBRARY_PATH}
  export LD_LIBRARY_PATH
to extend LD_LIBRARY_PATH if you already have it set.

Note that you may also need to set LD_LIBRARY_PATH to point at other items such as compiler run-time libraries, for example if you are using a newer version of the compiler.

If you are using a different compiler, you may need to link against the Intel icc run-time libraries provided in [INSTALL_DIR]/rtl.

3.2. Example Programs

The example results distributed were generated at Mark 26, 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 static library libnagc_mkl.a (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 by using one of the following scripts, which are located in the directory [INSTALL_DIR]/scripts.

Each command 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_mkl e04ucc
will copy the example program and its data and options files (e04ucce.c, e04ucce.d and e04ucce.opt) into the current directory, compile and link the program and run it to produce the example program results in the file e04ucce.r.

3.3. Data Types

In this implementation, the NAG types Integer and Pointer are defined as follows:
 NAG Type   C Type   Size (bytes) 
 Integer   long     8 
 Pointer   void *   8 

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).

3.4. Maintenance Level

The maintenance level of the Library can be determined by compiling and executing the example that calls a00aac, or you could call one of the nagc_example* scripts with the argument a00aac. See Section 3.2. This example prints out details of the implementation, including title and product code, compiler and precision used, mark and maintenance level.

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 may be included in the libraries libnagc_mkl.a and libnagc_mkl.so to avoid problems with the vendor version:

      None
    
  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   = 9223372036854775807
    X02BEC   = 15
    

5. Documentation

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.html
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_cl26/index.html

Advice on viewing and navigating the formats available can be found in http://www.nag.co.uk/numeric/cl/nagdoc_cl26/html/genint/essint.html.

In addition the following are provided:

6. Support from NAG

Please see

http://www.nag.co.uk/content/nag-technical-support-service

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.

7. Contact Addresses

Please see

http://www.nag.co.uk/content/worldwide-contact-information

for worldwide contact details for the Numerical Algorithms Group.