NAG Fortran SMP Library, Release 2


Silicon Graphics (IRIX 6) Double Precision

Users' Note


1. Introduction

This document is essential reading for every user of the NAG Fortran SMP Library implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Fortran SMP Library documentation. Wherever this documentation refers to the "Users' Note for your implementation", you should consult this note.

NAG recommends that you read the following minimum reference material which can be found in the documentation, together with this note, before calling any library routine:

(a) Introduction to the NAG Fortran SMP Library
(b) Essential Introduction to the NAG Fortran Library
(c) The appropriate Chapter Introduction
(d) The appropriate Routine Document

2. General Information

2.1. Accessing the Library

Assuming that libnagsmp.a has been installed in a directory in the search path of the linker, such as /usr/lib64/mips4, then you may link to the NAG Fortran SMP Library in the following manner:

(a) Set the environment variable OMP_NUM_THREADS to the number of available processors, e.g.

(for Korn and Bourne shell - ksh, bsh)

(for C shell - csh)
where N is the number of available processors.

(b) Compile and link with the Silicon Graphics Scientific Library (SCSL), multi-processor version, e.g.

f77 -64 -mips4 -r10000 -mp -o driver.exe driver.f -lnagsmp -lscs_mp
where driver.f is your application program.

In some circumstances you may receive a warning from the link editor concerning SCSL not being used for linking (WARNING 84). These warnings can be ignored or can be suppressed using the compiler option -Wl,-woff,84.

2.2. Example Programs

The example programs are most easily accessed by the command nagexample, which will provide you with a copy of an example program (and its data, if any), compile the program and link it with the library (showing you the compile command so that you can recompile your own version of the program). Finally, the executable program will be run, presenting its output to stdout. The example program concerned is specified by the argument to nagexample, e.g.
nagexample c06eaf
will copy the example program and its data into the files c06eafe.f and c06eafe.d in the current directory and process them to produce the example program results.

The example programs supplied to a site in machine-readable form have been modified as necessary so that they are suitable for immediate execution. In some instances they may differ from the example program supplied in the documentation. The distributed example programs should be used in preference wherever possible.

2.3. Interpretation of Bold Italicised Terms

For this double precision implementation, the bold italicised terms used in the documentation should be interpreted as:
real                 - DOUBLE PRECISION (REAL*8)
basic precision      - double precision
complex              - COMPLEX*16
additional precision - quadruple precision (REAL*16)
machine precision    - the machine precision, see the value
                       returned by X02AJF in Section 3  

Thus a parameter described as real should be declared as DOUBLE PRECISION in your program. If a routine accumulates an inner product in additional precision, it is using software to simulate quadruple precision.

In some routine documents additional bold italicised terms are used in the published example programs and they must be interpreted as follows:

real as an intrinsic function name - DBLE
imag                               - DIMAG
cmplx                              - DCMPLX
conjg                              - DCONJG
e in constants, e.g. 1.0e-4        - D, e.g. 1.0D-4
e in formats, e.g. e12.4           - D, e.g. D12.4

All references to routines in Chapter F07 - Linear Equations (LAPACK) and Chapter F08 - Least-squares and Eigenvalue Problems (LAPACK) use the LAPACK name, not the NAG F07/F08 name. The LAPACK name is precision dependent, and hence the name appears in a bold italicised typeface.

The typeset examples use the single precision form of the LAPACK name. To convert this name to its double precision form, change the first character either from S to D or C to Z as appropriate.
For example:

sgetrf refers to the LAPACK routine name - DGETRF
cpotrs                                   - ZPOTRS

2.4. Explicit Output from NAG Routines

Certain routines produce explicit error messages and advisory messages via output units which either have default values or can be reset by using X04AAF for error messages and X04ABF for advisory messages. (The default values are given in Section 3). The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified.

2.5. User Documentation

The following machine-readable information files are provided in the doc directory:

See Section 4 for additional documentation available from NAG.

3. Routine-specific Information

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

(a) D03

The example programs for D03RAF and D03RBF take much longer to run than other examples.

(b) F06, F07 and F08

In this implementation calls to the Basic Linear Algebra Subprograms (BLAS) and linear algebra routines (LAPACK) are implemented by calls to the Silicon Graphics Scientific Library except for the following routines where the NAG equivalent is used:

(c) G02

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

(d) G05

In this implementation the default mechanism used for generating random numbers is the parallelised set of Wichmann-Hill generators. This can also be selected manually by calling G05ZAF with its only parameter set to 'W' prior to any calls to G05 routines. Alternatively, the standard serial generator, as used in the NAG Fortran Library (Mark 19 or earlier), can be selected by calling G05ZAF with its parameter set to 'O' prior to any calls to G05 routines.

The default mechanism contains 273 generators. When OpenMP parallelism is requested by setting the environment variable OMP_NUM_THREADS to a value greater than 1, generators are used to generate independently portions of a sequence of random numbers. The generator assigned to each portion cannot be predetermined; therefore reproducibility of results should not be expected when using these routines in parallel. If reproducibility of random sequences is required, then the standard serial mechanism should be selected using G05ZAF.

(e) P01

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

(f) S07 - S21

The constants referred to in the documentation have the following values in this implementation:
S07AAF  F(1)   = 1.0D+13
        F(2)   = 1.0D-14

S10AAF  E(1)   = 18.50
S10ABF  E(1)   = 708.0
S10ACF  E(1)   = 708.0

S13AAF  x(hi)  = 708.3
S13ACF  x(hi)  = 5.6D+14
S13ADF  x(hi)  = 5.6D+14

S14AAF  IFAIL  = 1 if X > 170.0
        IFAIL  = 2 if X < -170.0
        IFAIL  = 3 if abs(X) < 2.23D-308
S14ABF  IFAIL  = 2 if X > 2.55D+305

S15ADF  x(hi)  = 26.6
        x(low) = -6.25
S15AEF  x(hi)  = 6.25

S17ACF  IFAIL  = 1 if X > 5.6D+14
S17ADF  IFAIL  = 1 if X > 5.6D+14
        IFAIL  = 3 if 0.0 < X <= 2.23D-308
S17AEF  IFAIL  = 1 if abs(X) > 5.6D+14
S17AFF  IFAIL  = 1 if abs(X) > 5.6D+14
S17AGF  IFAIL  = 1 if X > 103.8
        IFAIL  = 2 if X < -8.9D+9
S17AHF  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -8.9D+9
S17AJF  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -1.8D+9
S17AKF  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -1.8D+9
S17DCF  IFAIL  = 2 if abs (Z) < 3.93D-305
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
S17DEF  IFAIL  = 2 if imag (Z) > 700.0
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 1.07D+9
S17DGF  IFAIL  = 3 if abs (Z) > 1.02D+3
        IFAIL  = 4 if abs (Z) > 1.04D+6
S17DHF  IFAIL  = 3 if abs (Z) > 1.02D+3
        IFAIL  = 4 if abs (Z) > 1.04D+6
S17DLF  IFAIL  = 2 if abs (Z) < 3.93D-305
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9

S18ADF  IFAIL  = 2 if 0.0 < X <= 2.23D-308
S18AEF  IFAIL  = 1 if abs(X) > 711.6
S18AFF  IFAIL  = 1 if abs(X) > 711.6
S18CDF  IFAIL  = 2 if 0.0 < X <= 2.23D-308
S18DCF  IFAIL  = 2 if abs (Z) < 3.93D-305
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 1.07D+9
S18DEF  IFAIL  = 2 if real (Z) > 700.0
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 3.27D+4
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 1.07D+9

S19AAF  IFAIL  = 1 if abs(x) >= 49.50
S19ABF  IFAIL  = 1 if abs(x) >= 49.50
S19ACF  IFAIL  = 1 if X > 997.26
S19ADF  IFAIL  = 1 if X > 997.26

S21BCF  IFAIL  = 3 if an argument < 1.579D-205
        IFAIL  = 4 if an argument >= 3.774D+202
S21BDF  IFAIL  = 3 if an argument < 2.820D-103
        IFAIL  = 4 if an argument >= 1.404D+102

(g) X01

The values of the mathematical constants are:
X01AAF (PI)    = 3.1415926535897932
X01ABF (GAMMA) = 0.5772156649015329

(h) X02

The values of the machine constants are:

The basic parameters of the model

X02BHF = 2
X02BJF = 53
X02BKF = -1021
X02BLF = 1024
Derived parameters of the floating-point arithmetic
X02AJF = Z'3CA0000000000001' ( 1.11022302462516D-16 )
X02AKF = Z'0010000000000000' ( 2.22507385850721D-308 )
X02ALF = Z'7FEFFFFFFFFFFFFF' ( 1.79769313486231D+308 )
X02AMF = Z'0010000000000000' ( 2.22507385850721D-308 )
X02ANF = Z'0020000000000000' ( 4.45014771701441D-308 )
Parameters of other aspects of the computing environment
X02AHF = Z'4300000000000000' ( 5.62949953421312D+14 )
X02BBF = 2147483647
X02BEF = 15

(i) X04

The default output units for error and advisory messages for those routines which can produce explicit output are both Fortran Unit 6.

(j) X05

The finest granularity of wall-clock time available on this system is one second, so the seventh element of the integer array passed as a parameter to X05AAF will always be returned with the value 0.

4. Documentation

Each NAG Fortran SMP Library site is ordinarily provided with a single printed copy of all supporting documentation. If you require additional copies then please contact NAG.

On-line documentation is also provided, in PDF form, with this implementation.

5. Support from NAG

(a) Contact with NAG

Queries concerning this document or the implementation generally should be directed initially to your local Advisory Service. If you have difficulty in making contact locally, you can contact NAG directly at one of the addresses given in the Appendix.

(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 please quote your NAG site reference and NAG product code (in this case FSSG620DA).

(c) NAG Websites

The NAG websites are an information service providing items of interest to users and prospective users of NAG products and services. The information is reviewed and updated regularly and includes implementation availability, descriptions of products, downloadable software, product documentation and technical reports. The NAG websites can be accessed at

or (in North America)

or (in Japan)

(d) NAG Electronic Newsletter

If you would like to be kept up to date with news from NAG you may want to register to receive our electronic newsletter, which will alert you to special offers, announcements about new products or product/service enhancements, case studies and NAG's event diary. To register visit the NAG Ltd website or contact us at

6. User Feedback

Many factors influence the way 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. We have provided a short survey on our website at to enable you to provide this feedback. Alternatively feel free to contact the appropriate NAG Response Centre who will be happy either to record your comments or to send you a printed copy of the survey.

Appendix - Contact Addresses

Wilkinson House
Jordan Hill Road
OXFORD  OX2 8DR                         NAG Ltd Response Centre
United Kingdom                          email:
Tel: +44 (0)1865 511245                 Tel: +44 (0)1865 311744
Fax: +44 (0)1865 310139                 Fax: +44 (0)1865 311755
1400 Opus Place, Suite 200
Downers Grove
IL 60515-5702                           NAG Inc Response Center
USA                                     email:
Tel: +1 630 971 2337                    Tel: +1 630 971 2345
Fax: +1 630 971 2706                    Fax: +1 630 971 2346
Schleissheimerstrasse 5
85748 Garching
Tel: +49 (0)89 320 7395
Fax: +49 (0)89 320 7396

Nihon NAG KK
Yaesu Nagaoka Building No. 6 
1-9-8 Minato

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