NAG Fortran Library, Mark 19


Cray T3E Single Precision

Users' Note


1. Introduction

This document is essential reading for every user of the NAG Fortran Library Implementation specified in the title. It provides implementation-specific detail that augments the information provided in the NAG Fortran Library Manual and Introductory Guide. Wherever those manuals refer to the "Users' Note for your implementation", you should consult this note.

NAG recommends that you read the following minimum reference material before calling any library routine:

(a) Essential Introduction
(b) Chapter Introduction
(c) Routine Document
(d) Implementation-specific Users' Note

Items (a), (b) and (c) are included in the NAG Fortran Library Manual; items (a) and (b) are also included in the NAG Fortran Library Introductory Guide; item (d) is this document which is provided in HTML form. Item (a) is also supplied in plain text form.

2. Availability of Routines

All routines listed in the chapter contents documents of the NAG Fortran Library Manual, Mark 19 are available in this implementation. At Mark 19, 68 new primary ("user-callable") routines have been introduced, and 15 deleted. Please consult the file doc/news.html (see Section 3.5) for lists of these routines and for a list of routines scheduled for withdrawal at Mark 20 or later. Your suggestions for new algorithms for future releases of the Library are welcomed (see Section 7).

3. General Information

3.1. Accessing the Library

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

f90 driver.f -lnag
where driver.f is your application program.

3.2. 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 c06eae
will copy the example program and its data into the files c06eaee.f and c06eaee.d in the current directory and process them to produce the example program results.

In the NAG Fortran Library Manual, routine documents that have been typeset since Mark 12 present the example programs in a generalised form, using bold italicised terms as described in Section 3.3.

In other routine documents, the example programs are in single precision. All printed example programs show routine names ending in F not E (see Section 3.6).

The example programs supplied to a site in machine-readable form have been modified as necessary so that they are suitable for immediate execution. Note that all the distributed example programs have been revised and do not correspond exactly with the programs published in the manual, unless the documents have been recently typeset. The distributed example programs should be used in preference wherever possible.

3.3. Interpretation of Bold Italicised Terms

For this double precision implementation, the bold italicised terms used in the NAG Fortran Library Manual should be interpreted as:

real                 - REAL (REAL*8)
basic precision      - single precision
complex              - COMPLEX (COMPLEX*16)
additional precision - double precision (REAL*16)
machine precision    - the machine precision, see the value
                       returned by X02AJE in Section 4

Thus a parameter described as real should be declared as REAL in your program. If a routine accumulates an inner product in additional precision, it is using double precision.

In routine documents that have been newly typeset since Mark 12 additional bold italicised terms are used in the published example programs and they must be interpreted as follows:

real as an intrinsic function name - REAL
imag                               - AIMAG
cmplx                              - CMPLX
conjg                              - CONJG
e in constants, e.g. 1.0e-4        - E, e.g. 1.0E-4
e in formats, e.g. e12.4           - E, e.g. E12.4

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.
For example:

sgetrf refers to the LAPACK routine name - SGETRF
cpotrs                                   - CPOTRS

3.4. 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 X04AAE for error messages and X04ABE for advisory messages. (The default values are given in Section 4). The maximum record lengths of error messages and advisory messages (including carriage control characters) are 80 characters, except where otherwise specified.

3.5. User Documentation

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

See Section 5 for additional documentation available from NAG.

3.6. Naming of Routines

To ensure a single precision implementation is completely distinct from any double precision version also available, all single precision routine names have been modified by changing the sixth character from F to E. Thus, for example:
A02AAF  denotes the double precision version
A02AAE  denotes the single precision version

The names of auxiliary routines have also been modified by interchanging the first three and the last three characters, e.g. C02AFZ has been changed to AFZC02.

In the NAG Fortran Library Manual all library routine names end in F. Therefore, when using the manual in conjunction with this single precision implementation, all such names must be understood to refer to the single precision versions with names ending in E. Some routines in the Library require users to specify particular auxiliary routines. Again, when using this implementation it is necessary to specify the amended names, as given in Section 4.

The names of COMMON blocks have also been modified, e.g. AC02AF is renamed AFC02A. This is unlikely to affect the user.

3.7. Interface Blocks

The NAG Fortran Library Interface Blocks define the type and arguments of each user callable NAG Fortran Library routine. These are not essential to calling the NAG Fortran Library from Fortran 90 programs. Their purpose is to allow the Fortran 90 compiler to check that NAG Fortran Library routines are called correctly. The interface blocks enable the compiler to check that:

(a) Subroutines are called as such
(b) Functions are declared with the right type
(c) The correct number of arguments are passed
(d) All arguments match in type and structure

These interface blocks have been generated automatically by analysing the source code for the NAG Fortran Library. As a consequence, and because these files have been thoroughly tested, they are more reliable than writing your own declarations.

The NAG Fortran Library Interface Block files are organised by Library chapter. The module names are:

These are supplied in pre-compiled form (.o files) and they can be accessed by specifying the -p"pathname" option on each f90 invocation, where "pathname" is the path of the directory containing the .o files.

In order to make use of these modules from existing Fortran 77 code the following changes need to be made:

These changes are illustrated by showing the conversion of the Fortran 77 version of the example program for NAG Fortran Library routine S18DEE. Please note that this is not exactly the same as the example program that is distributed with this implementation. Each change is surrounded by comments boxed with asterisks.

*     S18DEE Example Program Text
*     Mark 14 Revised.  NAG Copyright 1989.
* Add USE statement for relevant chapters                         *
*                                                                 *
*     .. Parameters ..
      INTEGER          NIN, NOUT
      PARAMETER        (NIN=5,NOUT=6)
      INTEGER          N
      PARAMETER        (N=2)
*     .. Local Scalars ..
      COMPLEX          Z
      REAL             FNU
      INTEGER          IFAIL, NZ
      CHARACTER*1      SCALE
*     .. Local Arrays ..
      COMPLEX          CY(N)
*     .. External Subroutines ..
* EXTERNAL declarations need to be removed (and type declarations *
*  for functions).                                                *
C      EXTERNAL         S18DEE
*                                                                 *
*     .. Executable Statements ..
      WRITE (NOUT,*) 'S18DEE Example Program Results'
*     Skip heading in data file
      READ (NIN,*)
      WRITE (NOUT,*)
      WRITE (NOUT,99999) 'Calling with N =', N
      WRITE (NOUT,*)
      WRITE (NOUT,*)
     +'   FNU            Z        SCALE       CY(1)              CY(2)
     +   NZ IFAIL'
      WRITE (NOUT,*)
   20 READ (NIN,*,END=40) FNU, Z, SCALE
      IFAIL = 0
      WRITE (NOUT,99998) FNU, Z, SCALE, CY(1), CY(2), NZ, IFAIL
      GO TO 20
   40 STOP
99999 FORMAT (1X,A,I2)
99998 FORMAT (1X,F7.4,'  (',F7.3,',',F7.3,')   ',A,
     +       2('  (',F7.3,',',F7.3,')'),I4,I4)

4. Routine-specific Information

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

(a) D01

D01BAE  auxiliaries D01BAW, D01BAX, D01BAY and D01BAZ have been renamed as 
        BAWD01, BAXD01, BAYD01 and BAZD01 respectively

D01BBE  auxiliaries D01BAW, D01BAX, D01BAY and D01BAZ have been renamed as 
        BAWD01, BAXD01, BAYD01 and BAZD01 respectively

D01FDE  auxiliary D01FDV has been renamed as FDVD01

(b) D02

D02BJE  auxiliaries D02BJW and D02BJX have been renamed as BJWD02 and BJXD02 

D02EJE  auxiliaries D02EJW, D02EJX and D02EJY have been renamed as EJWD02, 
        EJXD02 and EJYD02 respectively

D02NBE  auxiliaries D02NBY and D02NBZ have been renamed as NBYD02 and NBZD02 

D02NCE  auxiliaries D02NBY and D02NCZ have been renamed as NBYD02 and NCZD02 

D02NDE  auxiliaries D02NBY and D02NDZ have been renamed as NBYD02 and NDZD02 

D02NGE  auxiliaries D02NBY and D02NGZ have been renamed as NBYD02 and NGZD02 

D02NHE  auxiliaries D02NBY and D02NHZ have been renamed as NBYD02 and NHZD02 

D02NJE  auxiliaries D02NBY and D02NJZ have been renamed as NBYD02 and NJZD02 

D02RAE  auxiliaries D02GAX and D02GAZ have been renamed as GAXD02 and GAZD02 

D02SAE  auxiliaries D02HBW, D02HBX, D02HBY and D02HBZ have been renamed as 
        HBWD02, HBXD02, HBYD02 and HBZD02 respectively

(c) D03

The example programs for D03RAE and D03RBE take much longer to run than other examples.
D03PFE  auxiliary D03PFP has been renamed as PFPD03

D03PHE  auxiliary D03PCK has been renamed as PCKD03

D03PJE  auxiliary D03PCK has been renamed as PCKD03

D03PKE  auxiliary D03PEK has been renamed as PEKD03

D03PLE  auxiliaries D03PEK and D03PLP have been renamed as PEKD03 and PLPD03 

D03PPE  auxiliaries D03PCK and D03PCL have been renamed as PCKD03 and PCLD03 

D03PRE  auxiliaries D03PEK and D03PEL have been renamed as PEKD03 and PELD03 

D03PSE  auxiliaries D03PEK, D03PEL and D03PLP have been renamed as PEKD03, 
        PELD03 and PLPD03 respectively

D03PWE  auxiliaries D03PEK and D03PLP have been renamed as PEKD03 and PLPD03 

D03PXE  auxiliaries D03PEK and D03PLP have been renamed as PEKD03 and PLPD03 

(d) E04

E04GBE  auxiliaries E04FCV and E04HEV have been renamed as FCVE04 and HEVE04 

E04NFE  auxiliary E04NFU has been renamed as NFUE04

E04NKE  auxiliary E04NKU has been renamed as NKUE04

E04UCE  auxiliary E04UDM has been renamed as UDME04

E04UGE  auxiliaries E04UGM and E04UGN have been renamed as UGME04 and UGNE04 

E04UNE  auxiliary E04UDM has been renamed as UDME04

E04ZCE  auxiliary E04VDM has been renamed as VDME04

(e) F02

F02FJE  auxiliary F02FJZ has been renamed as FJZF02

(f) 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 Cray Research libsci.a Subroutine Library. All calls to BLAS and LAPACK routines (except the sparse BLAS) use the code in libsci.a except the following, which use NAG versions:

(g) G02

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

(h) H02

H02CBE  auxiliaries E04NFU and H02CBU have been renamed as NFUE04 and CBUH02 

H02CEE  auxiliaries E04NKU and H02CEY have been renamed as NKUE04 and CEYH02 

(i) P01

On hard failure, P01ABE writes the error message to the error message unit specified by X04AAE and then stops.

(j) S07 - S21

The constants referred to in the NAG Fortran Library Manual have the following values in this implementation:
S07AAE  F(1)   = 1.0E+13
        F(2)   = 1.0E-14

S10AAE  E(1)   = 18.50
S10ABE  E(1)   = 708.0
S10ACE  E(1)   = 708.0

S13AAE  x(hi)  = 708.3
S13ACE  x(hi)  = 3.3E+7
S13ADE  x(hi)  = 3.3E+7

S14AAE  IFAIL  = 1 if X > 170.0
        IFAIL  = 2 if X < -170.0
        IFAIL  = 3 if abs(X) < 2.23E-308
S14ABE  IFAIL  = 2 if X > 2.55E+305

S15ADE  x(hi)  = 26.6
        x(low) = -6.25
S15AEE  x(hi)  = 6.25

S17ACE  IFAIL  = 1 if X > 3.3E+7
S17ADE  IFAIL  = 1 if X > 3.3E+7
        IFAIL  = 3 if 0.0 < X <= 2.23E-308
S17AEE  IFAIL  = 1 if abs(X) > 3.3E+7
S17AFE  IFAIL  = 1 if abs(X) > 3.3E+7
S17AGE  IFAIL  = 1 if X > 103.8
        IFAIL  = 2 if X < -1.3E+5
S17AHE  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -1.3E+5
S17AJE  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -1.3E+5
S17AKE  IFAIL  = 1 if X > 104.1
        IFAIL  = 2 if X < -1.3E+5
S17DCE  IFAIL  = 2 if abs (Z) < 5.97E-154
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 6.71E+7
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 4.50E+15
S17DEE  IFAIL  = 2 if imag (Z) > 700.0
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 6.71E+7
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 4.50E+15
S17DGE  IFAIL  = 3 if abs (Z) > 1.65E+5
        IFAIL  = 4 if abs (Z) > 2.72E+10
S17DHE  IFAIL  = 3 if abs (Z) > 1.65E+5
        IFAIL  = 4 if abs (Z) > 2.72E+10
S17DLE  IFAIL  = 2 if abs (Z) < 5.97E-154
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 6.71E+7
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 4.50E+15

S18ADE  IFAIL  = 2 if 0.0 < X <= 2.23E-308
S18AEE  IFAIL  = 1 if abs(X) > 711.6
S18AFE  IFAIL  = 1 if abs(X) > 711.6
S18CDE  IFAIL  = 2 if 0.0 < X <= 2.23E-308
S18DCE  IFAIL  = 2 if abs (Z) < 5.97E-154
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 6.71E+7
        IFAIL  = 5 if abs (Z) or FNU+N-1 > 4.50E+15
S18DEE  IFAIL  = 2 if real (Z) > 700.0
        IFAIL  = 3 if abs (Z) or FNU+N-1 > 6.71E+7
        IFAIL  = 4 if abs (Z) or FNU+N-1 > 4.50E+15

S19AAE  IFAIL  = 1 if abs(x) >= 49.50
S19ABE  IFAIL  = 1 if abs(x) >= 49.50
S19ACE  IFAIL  = 1 if X > 997.26
S19ADE  IFAIL  = 1 if X > 997.26

S21BCE  IFAIL  = 3 if an argument < 1.579E-205
        IFAIL  = 4 if an argument >= 3.774E+202
S21BDE  IFAIL  = 3 if an argument < 2.820E-103
        IFAIL  = 4 if an argument >= 1.404E+102

(k) X01

The values of the mathematical constants are:
X01AAE (PI)    = 3.1415926535897932
X01ABE (GAMMA) = 0.5772156649015329

(l) X02

The values of the machine constants are:

The basic parameters of the model

X02BHE = 2
X02BJE = 53
X02BKE = -1021
X02BLE = 1024
Derived parameters of the floating-point arithmetic
X02AJE = Z'3CA0000000000001' ( 1.11022302462516E-16 )
X02AKE = Z'0010000000000000' ( 2.22507385850720E-308 )
X02ALE = Z'7FEFFFFFFFFFFFFF' ( 1.79769313486232E+308 )
X02AME = Z'0010000000000000' ( 2.22507385850720E-308 )
X02ANE = Z'2010000000000043' ( 2.98333629248013E-154 )
Parameters of other aspects of the computing environment
X02AHE = Z'4180000000000000' ( 3.35544320000000E+7 )
X02BBE = 9223372036854775807
X02BEE = 15

(m) X04

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

5. Documentation

Each supported NAG Fortran Library site is currently provided with a printed copy of the NAG Fortran Library Manual (or Update) and Introductory Guide. Additional copies are available for purchase; please refer to the NAG documentation order form (available on the NAG websites, see Section 6 (c)) for details of current prices.

On-line documentation is bundled with this implementation. Please see the Readme file on the distribution medium for further information.

6. 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. Users subscribing to the support service are encouraged to contact one of the NAG Response Centres (see below).

(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 FLCRE19SE).

(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 simply visit one of our websites or contact us at

7. 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